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<h2>HL Paper 2</h2><div class="specification">
<p>A longitudinal wave travels in a medium with speed 340&thinsp;m&thinsp;s<sup>&minus;1</sup>. The graph shows the variation&nbsp;with time <em>t</em> of the displacement <em>x</em> of a particle P in the medium. Positive displacements on&nbsp;the graph correspond to displacements to the right for particle P.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbkAAAGSCAYAAAB+P7/dAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAEHnSURBVHhe7d0JeFTl2Tfw/5vyYZXlohQVoeRFakSiFA0IVpRFViPQCKJUwUKBgALRWFBJlPKqAVEkEhYRqCBBRV4guRAoi8iiocoS4xaEWMR5A0YFpCFQpZj55n5yDknGDLPkzJxl/r/rynWSeybnSSAz9znPcj//5fYAERGRA8VoRyIiIsdhkiMiIsdikiMiIsdikiMiIsdikiMiIsdikiMiIscKS5IrL1qKAW2mYHtpuRYhIiKKvDAkuR/wz7wtKBp4GxIa8kaRiIjME4YsVIYjRSWIi7sC9bUIERGRGQJLcuUHsHRAD6RvP6YFPKGjuRjbpjX6Zu7xpLUqSj/FljVNMbDzf3PAj4iITBVYHoq5Er3/fB3WzFqHIhlmK3dh7VPTsKPrDLzy0I1V7tjKUZr/DtbE9ULn3/5Si3mU5GJU7O8wKvf/tMA5T2g8YmPHI7fknBYrQ35mH8TeOxMrF6ag65W/8TyegMEztsJ1dDdenfQHXB/riV3ZEymvfYIyFiMjIiI/ArzZqotmPYci+Ww2lu4sQv7sh5ByeABempqIZtXOcBbfHP4n0LYlLg/1Nu69V7DUdSvm7C7AjgV34vSC0RiQOBl5V6djy4F9WDOxBTZMfgKLPvyX9g1EREQ1CzwV1W+LfkOaYs2z4/FoJpA6bTy6Na2rPagp/wp5a0owsNd1aKiFglYvCamPDMTvLm2CK2+/F/fd+EuciB2GSSM74tKLL0eHYX/CPfU+wYa9xfhJ+xYiIqKaBHG/9Uv8tnMvxBV+j5ZPPYPRCY20eKXyf/4Da4o6o1dCYy0Sgoua4NcNf1Hx+X/VRb2GdYDLGqGB/pNe0hBNLjqL707/CPZYEhHRhQSe5Mo+w7IZ81GAo8gr+g4/XwFXjrIjh1AU1wrN64faV0lERGScALPRSeQvegJTioci9/1XMXDNIs8d2w/aY7oTyN+Sh7iBv8dvmeOIiMgCAkhHZ3E096+4b+HleGr2cCQ0a49ByWcwY+n7KNWeofhdOnACeeu240DZOZQVrcOcBVs8sQLs+fxrFGX/jdVRiIjIcH6SXDnKDryJKZP/ga7T03B/a5lO0gjX9/sD4tbk4J2jZyue5lH+zWF8gt+i5eVek1E0dXrfhwHFz6BXfEvcOMOFbpMeRWK9w8i+/0EsbXALOrA6ChERGey/3B7a52FSjtLtU9FpViuszR2OOOYyIiKKkAiknIq1c6cL9uKzb/WF30REROEXgSQXg3qNmqBevcZodAlv44iIKHIi0F1JRERkDt5aERGRYzHJERGRYzHJERGRYzHJERGRYzHJERGRYzHJERGRY4VlCUFs7G+wdMmr2ldERGQnt/XooX3mAJLkjNaiRXPts+q2vv229ll1wcaFUecyKy7MajvYuDCrbaPiwqy2jYoLs9o2Ki7MatuouDCr7WDjwshz2RG7K4mIyLGY5IiIyLGY5IiIyLGY5IiIyLGY5IiIyLGY5IiIyLGY5IiIyLGY5IiIyLFY8YSIiKphxRM/WPGkkq+4MKvtYOPCrLaNiguz2jYqLsxq26i4MKtto+LCrLaDjQsjz2VH7K4kIiLHYpIjIiLHYpIjIiLHCjDJnUVJ/mtI79taTSqJje2IUZlbUFRWrj1ORERkPQEkuXKU5S/A8KTZOD52Cw67iuEqnIdrN43HgOk7Uao9i4iIyGoCSHJncHDHehSiI/re1KziG+q3Qdc+LXE6exXeKTmnnkVERGQ1HJMjIiLHCiDJXYKru96BeOzGxvePQo3Cle3Hjk2HUS+xJzpeVkc9i4iIyGoCrHjyA4qWjkSPKTu0rz3q/RnLPpiKbg1/nidlcoovrIRCRGRtUVbx5Ef3kZwU9zXXjHEv+fxfFaGfjri3PdnP3aLPbPe+Uz9VxKpgxZNKvuLCrLaDjQuz2jYqLsxq26i4MKtto+LCrLaNiguz2g42Low8lx35764s3YV5k1cDA4dgYOuGFbGYZugybBCuL1yM+W8fqYgRERFZjP8kd+YkvjkNXNSkIS7RQiKmQSNchhPY++V34PxKIiKyIv9Jrkksrm2sfV5F+amT+BaN0eHKS8GpJ0REZEX+k1yd63DP1EH4cdNqvJFfUjG7svwodmavRkH8KDzYs7l6GhERkdX4T3Koi2ZJT2PtpMux474OaCllvVp2x7M/DUHu0rFIqB/AKYiIiEwQYIZqiLgeKVi8vxguKevlOoCNGfchoWld7XEiIiLr4W0YERE5FpMcERE5VoAVT4IjFU9Y2YSIyJ6irOJJ8FjxpJKvuDCr7WDjwqy2jYoLs9o2Ki7MatuouDCrbaPiwqy2g40LI89lR+yuJCIix2KSIyIix2KSIyIix2KSIyIix2KSIyIix2KSIyIix2KSIyIix2KSIyIixwpbxRNvrIBCRGQPrHjiByueVPIVF2a1HWxcmNW2UXFhVttGxYVZbRsVF2a1bVRcmNV2sHFh5LnsiN2VRETkWExyRETkWExyRETkWExyRETkWExyRETkWExyRETkWExyRETkWExyRETkWExyRETkWGEr68UyXkRE9sSyXn6wrFclX3FhVtvBxoVZbRsVF2a1bVRcmNW2UXFhVttGxYVZbQcbF0aey47YXUlERI7FJEdERI7FJEdERI4VcJIrL9mD7PT+alKJfLQZtQB7Ss5qjxIREVlPYEmubA9mD0/FjrhnUegqxuHdr2JwcSYGDV+A/LJy7UlERETWEkCS+wFFq15E5le3YejANqjvicQ07Y6Jj9+DeoXrsePgmYqnERERWYz/JFf+FfLW7EW9gbchoaH+9Bg07PYU9rs2ITVB0h4REZH1BJDkTuN712lc1OgkPs0aiTZqTK41+qa/hvwLjMm9/fYWFBUV4d///rcWISK7kdfwrl271If+mj5x4oT2KJH1+a94UpKLUR3HYzOaoffEF/HM+JvRFEexfeoY3L+7F3JXjUdC/eq5Uiam+MJKKETWdujQIezduxcb/r5ei/xcXNzV6N6tO9q2bYsGDRpoUXKK6Kp48nWOe2SL5u5rxuS4j/ykxTx+OrjE3b9FZ3fatu+0SCWpeHLmzBn3wYMH3Vu2bHaPHTtWxRISbnDn5OSox6oycxW/WXFhVtvBxoVZbRsVF2a1bVRchLONgoIC9223dVev1cGDB7uzs7NVrLi4WD2/6mt68uTJ6nnyIc8L9DUtjPhZhVlxYVbbwcaFkeeyI//dlZc0wuX1gItax+KyKs+OadAIl+Ew1n/owjktVtXFF1/sudqLQ8+evfDSSy9h69ZtiG8Tj5SU8fjTn/6kuj2IyHwypDBjxgz073+H+nrFipVYuXIlhg4dinbt2qF58+YqXvU1PW3aNBQUfIy7Bg1GWtrj6Nu3Dz766CP1PCIr8Z/k6l/h+cP2ZLka1UPsr+oFMkVTvThGjBihkt0335SgR4/uyM3N1R4lIjMcOXJEJah58+YgK2su0tPScfPNN2uPXljjxo3Rr1+/igvY+GtVkly+fLn2KJE1+M9PMb9Gy7aX4sS2j/FllSVx5adO4ltcirYtfx1QktNJstu4cZPnKvF+dVcnd3lEFHkymeT3v++kPpdElZSUpD4PlrymZ82ahcmT09VdXVpaGs6eZaEIsoYA8lMTdBk3EYlF8/HCWhdUnis7gLVLV6MocSLGdWminhUM6faQ7g55UUyfnoElS5ZwFiZRBBUWFmLIkLtxxx391UWnJKrakNf0Aw88gFdeWeK5m1uGlxe+zNc0WUJAN2ExzQZg5toMtF53F1rKEoL4YVjXJAVrZw5As2Bu47zIi0IS3Y6d2/H0009rUSIKJ7mDe+75GSrByR2YJCijyHidjOnt27cXjzzyCBMdmS7AFBWD+nG9kLp4N1yuYs/HbixO7YU4r6UDoZBEJ4PXcvXHrkui8JIEJ3dw7dt3MDzB6WRM79FJj2H9+reY6Mh0tc9SBpDBa73rkgPXROEhM5r1LsoxyWPCkuB08fHxqutSEt3SpUu1KFHkWSLJCbmjGzdughq4lqtNIjKOzKIcNWokrryyFTIyMlC3bl3tkfCRrkv94pUzqcks/iuehEAqnoRS2URmZMmAtcvlwmOPPoYmTYKf1EJE1emvKxknm/n8CxF/Xc2ZO0e1PeXJv6JVq1ZalKwsuiqehECqINQkkBX2Ul2hS5dbVcWFv2/YoEV/zqhV/GbFhVltBxsXZrVtVFyY1bZRcRHKuebPn69ek1KpRBfKeWoSSFyqochrWj6OHz8e0barMiouzGo72Lgw8lx2ZJnuSp1UV5g+/Vm8//4ubN68WYsSUSikDqV0F8pQgHQfmkHG/hYv/hu+/PIQZs6cqUWJIsNySU7I7Cx5Ua5a/b8sFUQUItkt4KUFL+Gmm25GSkqKFjWHrMOTiioyizo/P1+LEoWfJZOckBelVDpPSZnAKchEIZC7pu+++1ZNNAnnTMpASUUVmdmZNWe2mghDFAmWTXLyohz+p+GqiyMrK0uLElEgZO83uWsaNvT+WlczMdITTzyhjvPmzVNHonCzbJITMj4nU5CleCy7LYkCIz0fUkFIuilvvfVWLWoN8ppOHj1GJWBJxEThZukkJ4YPH35+bQ+7LYn8k54P6QGJ1Hq4YMmYu3RbSiLma5rCzfJJTrot9dmWmzZt0qJEVBOpaiI9H9IDYqVuSm9S7ksSMauhULhZPskJufLTt+aRGWNEVDOpRyk9H9IDYmWSgPVqKNxAmcIpbBVPvIVSAaWqY8eOYeKkvyDx9jtw9913a1Ei0snUfJm5mDLhISQkJGhR65JKLOlPpHveL2IxYfwELUpWwIonftSm4klV3nG9csPBgwdrfS6dWXFhVtvBxoVZbRsVF2a1bVRc+HpMqgPplYKqCvfPFGxcVH0sJydHvabz8vLC3rZRcWFW28HGhZHnsiNbdFfq9Eko0iVDRJX27t17frKJncjaOZkF+uKLL3I3cQoLWyU5mYSSmvqI2r5DdjYmoorKJgsXvazGra082cSXhx9+WE0sk0RNZDRbJTnRp08fdeWXk5ujRYii25tvvqmOI0aMUEe70SeWyWuaSwrIaLZLcnI3J1d+RUUHue8cRT25i5MZirK7vh3v4nSSoKUEGZcJkdFsl+SEXPlJXUvpxyeKZvpdXNeuXdXRriRBd+3SDZmZs3g3R4ayZZITdybdqfrxWRqIopV+FyfrzRo0aKBF7at3795q8gzv5shItk1y8fHxamxOSgMRRSP9Lu6ee+5RR7uTupYyNse7OTKSbZOckLE5ufLj2BxFm6p3cY0bN9ai9idjc7ybIyOFreJJbSucBCpjWsW6oPS0dHUkigbr1q1TmwrPyZrriK7KqpYsWYLC/YXIeMaaBaajASue+BGuiidV6Y9JpQS9YoIwqo1wx4VZbQcbF2a1bVRcmNW2UXEhjx0/flz9zUsFIF242zYqLvx9j1Q0kt9PqqEIo9o2Ki7MajvYuDDyXHZk6+5KITMt9YoJRNHAaWNx3mSmJcfmyCi2T3JCr5jAsTlyOil9JWNx48ZNcNRYnDeOzZFRHJHk5G5OalpmZ2drESJn0ktfDRw4UB2dSu7mZGPV119/XYsQhcYRSU7oNS2PHDmiRYicRbrupPSVXWtUBmvYsGGqh4Z1aqk2QkhyJ5GfeSdiY8cjt+ScFjOf1LSUu7nNmzdrESJn+fDDD1XpK6eOxXnTx9tZp5ZqI8gkV46y/GVIy9yjfW0dUtNy9Ohk7Ni5nbuHkyPJ5CopZ9euXTst4nzJyaNVnVruHk6hCi7Jle3DorR5sGrnQWJiojrqs8+InOKjjz5SXXdSzi6adO58Cy699DK1do4oFEEkuZPIXzQNmbgHqcNaazFrkdlmUo1dZp9x6jE5iVy4SXf8VVddpUWig/TQ9O3TF8uXL2MPDYUkwCSnd1MCqdNGo2uTOlrcem644QZ15NRjcgqZTCVv8jK5KhorgHTs2FEd2UNDoQisrFfZHmTeNRKb+vwNq1Lb4GDmICRlxiFr94tIavrzhCdlvXyJRLmvOXPnoLS0lKW+yBGcXMIrUPq/wcKXF7HUVwREWVmv7937ZiW5W/SZ7d536ifP16c8X/d2t2gxzp3z9X8qnuIlkmW9vEncu9SXMKpto+LCrLaDjQuz2jYqLsxquzbxM2fOVCvhFcm2qzIqLkI5l17qa8uWzVo0tPPUJNi4MKvtYOPCyHPZkZ/uyqrdlPcjoX6QkzFNoi8Ol6s/IjvLy3tPHXv27KmO0UpfHL5w4SItQhQYP1nrDA7uWI9C7EFm0nWqGzI29hokZX7meSwXKR0TMCr3/yqeajEyfiHjGFwcTnYmb+qyViwaFn/7oy8Ol5mmRIHyk+TqIyF1E1yu4iofnyM39VrPY0nI2p2PxUktKp5qMV26dFHHtWvXqiOR3ejLBqQ2K1VMKpMeGk5AoWDYo/8xBLKcQIrYrljxBpcTkC1t3LhRvanrM4ajnV7wgcsJKBiOTXJCithKJXMph0RkJ/ImPm/eHAwZ8kf15k4V9IIPGzZsUEcif0JIcnoX5twalw9YiYxjcK85sqOdO3eqY7TUqQyU9NBIgepFixZqEaILc/SdnJDadzKuwQkoZCeyxYy8mTt5z7hQ9evXT/XQcHcCCoTjk5zUvhPssiS7OHTokLowkzdz+jl9idAHH3ygRYh8C6ziSZBkqUEkKpsEStbL7di5AxnPZLBaAlneypUrsWfvHjz/3PNahLxt3boV2cuXRXUVmHCKsoonwTO74ok3vVpC1QooOqN+pmDjwqy2g40Ls9o2Ki7MajuY+PHjx9XfanZ2thapzoyfSRgVF0ac60L/TkacX/iKi3C3YVRcGHkuO3J8d6WQCSiyD5fnBaFFiKxJn3DSvXt3daSayVhl1y7dOAGF/IqKJCdu73s71q9/ixNQyNJkwkn79h3QvHlzLUK+dOrUSU1AYQUUupCoSXJ6WSRWQCGrkt2vZcJJj9scNB4SRvHx8WoCiiyaJ/IlapKcDE7rFVCIrOjtt99Wb9rRtjFqbUgFFFk0zwoo5EvUJDnRt29f1b2xa9cuLUJkDVJ6Tna0lwonnAEcOH3sMj9/nzoSeYuqJNeuXTt1pfzuu+9qESJr0NdxRvuWOsGSsUtuwUMXElVJTrB7g6xIZv5yS53QDBo0kFWNyKeoS3Ls3iCrkQsumfl77733ahEKhl7ViJPKqCZhq3jizUoVUObMnYPS0lKkp6VrESLzsHpH7bFKjLFY8cQPq1U8EVXjW7ZsVj9jcXFxrc5TVbBxYVbbwcaFWW0bFRdmte0vPnjwYPfkyZPV58LX84XRbXsLd1yEo42CgoLzVY3CcX5v4W7DqLgw8lx2FHXdlYLdG2QV+u7fLMZcO5xURr5EZZKTTSi5Zo6sQJazyJszd/+uPX1S2alTp7QIUZQmOaGvmeOeVGSWs2fPqgst7v5tDH1SmVSOIdJFbZLTuzc+/fRTLUIUWV988YW60JL90aj2ZM2cLMPI25WnRYiiOMkJuYLe8Pf1qtoEUaTJBZa8KcsFFxkjOXk09u3byzVzdF5UJ7kBAwaoY17ee+pIFCmyNk4usPS/QTJGQkJ7ddy2bZs6EkV1kpPuDdlnbvXqNVqEKDL0YgTcN85Y+j5znDlNuqhOcuKmTjepahMs80WRJBdW3DcuPGSfOVmWwX3mSISt4omVKpxciEw3npAyHsmjx3ACAEXEsWPHMHHSX5Ay4SEkJCRoUTKKzFpNHjMadw0azPWHIWLFEz+sXvGkKomPHTtWVZ2oysjz+xLuNoyKC7PaNiouzGrbO56dna1eI7k5OVqkOl/nEeH6mXThjotItP3ss8+6u3S5VYtUMOr8wqhzhTsujDyXHUV9d6VgFXOKJBkvku1hWKcyfPR1sOyyJCY5D87IokiRhcpyQTVs2DAtQuGgr4PduHGjFqFoxSTnITOyhg69nzOyKOzefvttdWQZr/CTdbBS5ovrYKNbYEmuvAT52enoG/sbNakkNrYjRmXmIr/krPYE+5MBas7IonCTMl5SN5VlvMJPn0im77pO0SmAJHcS+bMfQNK0EiSu3ovDLhcKt6bh8k2PIWn4AuSXlWvPszf9yloK5hKFg1xAyTjRrbfeqkUonLgzAQn/Sa60AKsX7kHj5HF48Mamnm+IQf24AXjs8XtQr3AlVu91xvoy7kxA4cYdByKPXZbkP8k17IaM/cUoSE1AHS0k33ZJw0a4CKX45qRz/njkCpszsigc5E2WOw5EHkv3UYgTT37Alx/vwwlcgWtjf6XF7I9dlhQuMi7EHQciT9+ZgKX7oldoSa7sE6xbsRe4/o/od319LWh/coU9eXI6uyzJcDIuJF2V3HEg8uRuTkr3cTPV6BRCWa+TyM8cgaSFscja+jySmtXV4pVkBqYvVi/3dejQITz19P/g0UmPIT4+XosShY5lpszFMmrBi+KyXv9yf75kjPuaFknuWfu+12I/Z7eyXt6kHNCY5GTtq+qMalcYda5wx4VZbRsVF2a1PScrS70mCgoKtEiFYM8jjPqZzIoLM9qWsn1JSX/Qvqou2PMLI34mEe64MPJcdhR4d2V5CfZkpSJpyhEMXjYPDyU00h5wHm6mSkaSzVHZVWku6bKUzVS520j0CSzJlX2GpckDMGjmt54E9zKmdmsW6owVW+AiUjKKXCjJBZNcOJF59H379H38KHr4z1XlLuROHIEpm4HErHmOT3BCrrgvvfQyLiKlWtMvlDir0lzcIDl6+c1X5wpWYeqGo57PjmJDys1oeb60V8XH9Zn5OFfxVEfp2qUrF5FSrcmFkry5sqvSfLf3vZ0bJEchv0muTsIjKHAVw+Xjo/oicefQZ1ayy5JCJRdIcqEku8+T+eLi4tRx586d6kjRwek9jyFr1aoV695RregXSLyLswbZv0/28Xv99de1CEUDJrkLYN07qo1169apahtNmjTRImQ2bpAcfZjkLoCzLClUMu6zfPmy87UTyRq4QXL0CaHiiX8yIcXqlU0CNenRSbixw424++67tQiRf/n5+ciaMxszn3+Bd3IWM2fuHJSWliI9LV2LkLcorngSGLtXPBF6fP78+er3OXPmjPraqPMLo84V7rgwq22j4iKSbY8dO1ZV2RBGnV8YdS6z4sKstvX4li2b1Wu6uLhYfR3seUSobXsLd1wYeS47YnelH+yypGBJV6VMVWdXpTWxyzK6MMn5ITPjOMuSgqFX1dCrbJC1NG7cWM2yXLt2rRYhJ2OSCwBnWVIwpKqGzKqUKhtkTZxlGT2Y5ALALksKFLsq7YFdltGDSS4A7LKkQLGr0h7YZRk9mOQCpHdZygaYRL688842dlXahN5lKZuqknMxyQVI77L84osv1JHIm1wAcQG4fehdlh999JE6kjMxyQVI77KUDTCJaqJfALGr0h70LsvC/YVahJwobBVPvDmhAorUIly1+n+x8OVFqFu3rhYlqrBy5UoUfVHESho2olemmZM1VxVwpgqseOKHkyqeVFVQUKB+t7y8PC1SKdjzCyN+JhHuuDCrbaPiIpxtSEUc+dvIzs7WIpWMalcYdS6z4sKstmuKHz9+XP2/SRUUb77OI8L5Mwmj4sLIc9kRuyuDIF2W3DGcaqIvL+nUqZM6kj1Il2X79h24Y7iDMckFiTuGU03kwkcugPSNOck+2ie0547hDsYkFyTuGE7e9B3A5QKI7Ofqq69WR32NIzkLk1yQuGM4edMvePQLILIX2QpJ1jayy9KZmORCwFqWVJVc8MiFj1wAkT3J2kZ2WToTk1wIWMuSdHpXpVz4kH3paxvZZek8THIh0BeGs1IC6Rc6+oUP2ZOUYWOXpTMxyYVIrtxXrHhD+4qild5VKRc+ZG/ssnSmsFU8cUKFkws5dOgQnnr6fzDlyb9yLCZKSa3K5DGjcdegwejXr58WJbuSQs0TJ/0FKRMeQkJCghaNTqx44odTK54IPa5XuJg/f776OtjziFDb9hbuuDCrbaPiwug2pPKN/A1IJRxh9PlrEu42wh0XZrUdSHzw4MHusWPHqs99PV+Eo+2qjIoLI89lR+yuDNHFF1+MceMmsMsyismYLLsqnYVdls7DJFcLt956K7788hAnoEQpucDhrEpn0WdZfv755+pI9sckVws33HCDOu7atUsdKXrIhY1c4HBWpbPosyxZ7CFUpSjaugbb//mD9nWl8qKlGNBmCraXlmuRyAgsyZWXID87HX1jf6MmlcTGdsSozFzkl0T3Ltnssoxe+oUNuyqdR7osZe2jTCyiYJSjdPtMDBhfAFzqvRXZD/hn3hYUDbwNCQ0je28VQGueH3znfNyX/jHaZ21FoasYh3dPR7NNjyEp+XUURTYpW47eZTl8xJ+0SHSJxt9bfme5sJELnGgRTf/Pbdu2VUeZORuNQv+/PotvDv8Tp+NaoXl979RShiNFJYiLuwL1tUikBJDkTiB/yzs4ff0gDB/QWv2AMU07Y9iQDkDBXnz27bmKp0UpvcuSootc2MgFDjmPXuyBgnEM29N7oseUHZ688AR6XOvVLVn6KbasaYqBnf+7MumU5GJUbGv0TZ+LzFEdK3sJs95D0YEtVWL9kZ57wJMmK5SX7EF2en/tMc9Hm5HI3Fp0/nFv/pPcORc+XH8Y9dq2xOXnn/1LXPm79miMAuz5/KQWi056lyVFH17gOJc+oYj1aQPVBN0eewbD6rXEsGUFcO1/Ct3Od0uWozT/HayJ64XOv/2lFtOdRmH2Jnw/NBeHXZ8iN7U5Ns8cgh5JK/CLMWtx+PBuLBsOZKc8hVVFP3hOdQDLkocifV8v5Ba64HIVYstj/w8LR4zA9O3HtHNW5z/JnSnFsR+Bi5o0xCVaSMQ0aIxYlOKbk/wj0K/ojxw5oo7kfHJhIxc45EysTxu88m8O45PT/4245t4dkhXdmKh2o1Sp3rC/YGK3Zp5k1AjX9/sDrpfYwGEYfmNTxMQ0wy1J3T03VJ/gvc++A77dj/cKTqNe+9/hKtUl2hCthy/Aftd7yOjWRJ3Pm/+KJ3JL2XE89qau9XwkoI4WrohPAbLWY3FSCy1YQW4hiYjInlyuYu2zQMmkk6no9ADw0gdTq9zFeXjuvpYmPYiiR96snohqyi015JVz+bPQIWkpOkhsgBu5D96FlA1A79RH0O+G9ujZLe7C43xqSfiFfJ3jHtmiubvdrH3u/2ghRcXbukfmuLRApWioeOJt6H33qWoJ3nw9X4T7ZzIqLsxq26i4MOJcUuFG/r6l4o03I84vfMVFuNsId1yY1Xaw8dSHHzbt/9qouDDyXL79231wyb3uFv2XuA/+pIU0Px1c4u5/zZPubf/yeqCm3FJDXvnPvhfc7arGTh10b8tZ7E7rc7X6/2nR4kb3yFk57n1f/1jxuBf/3ZWXNMLl9bTPqyg/dRLfap9TxWD1++/vYpelw8msysTb72BXZRTQN8Fll2UgZPbkV15zN0Q5yo4cQlGNMy5DVD8O3ZJGImPjAbgKt2HZU71QnDke983ZhVLtKVUFkOQaoslFwI/HSnFGC4nyUyfgQkNc3ogvdhEXF6eO27ZtU0dyHrmAkVmV1113nRYhJ5PC69xSK0Dlx3H4k4swsNd1nqxQlczOz0PcwN/jtwbluGok4Q0fi7G9G+P0J4fxTQ1L2vw3WycWN9zR0usEP+DLj/d5fvyaBhmjU4MGDXDHHf2xdu1aLUJOo1/AXHXVVepIzscttQJU9jWKin7UvqiipqUDtVB+NBdj28iyg1wUlUlC8twpHtiOdXk/Ir77tbiihkYCaLcxEnrdhnoF8zFj2Weem1LPSYs2YumKvaiXOBi9fzYlNHoNGjSQXZYOJhcwQ4fej7p1vas5kFPJLEvWpw1A/avRa/CvkH3/9WiTvv18t6GacYnfouXlxrxmYpolYuprM9Dnm2noER+L2NhYxPdaicvTlmPpQzfWOAElgCQXg4ZdHsRrGb1QPKUP4uWkPR7DvvZT8NrURDQzIj07REJCe3Vkl6XzyIWLXMDcdltFAV+KDldffbU6sj6tHzHN0O2pt9SszP0Z3c53WcbEDcfaamvmqmiahMWe5xdUnbWvYh9Xm7FfJ+ERFJyP1UXThCSkLt6t2qr4eAsZw25EUx+5KLAUFdMUCcMysPH8SQ9gY8Z9SGjKK9qqGjduzC5Lh9IvXPQLGYoOrE9rf7wPMxi7LJ1JLlzkAkYuZCi6cEste2OSM0Q5/v1FLvrGjkfJbyqq0u/fX6iOjuO1I8XwEQ87fkcKvasy8aYrVT09KWAblTtxlO1BZt/WiB2VixIt5DiqnqL+ty3/z7/BkCF3q4fec3CXZdV6kPJ7txm1AHsc8rfNJFdrMrvnNSx4PgeS1uo3quiyXL16TcXDjnIS+bMfQNK0EiSu3ovDLhdeeuZuXC47UgxfgHw128l59K7KNdMXY9Plach4aUnlThwO/r2rO438RdOQWXha+9qJylH6eT7y0BVPbf0CS5e8en7cR7osVzq1y9Jz8TJ7eCp2xD2rdpl55YWHMbg4E4Mc8rftv6xXCORqQP5AHK/8BIq2rcVrnzTCTY3ex4odLZD8wljg8w+wcNHLmJM1Vy0tcIwzH2Fp6izs6fMEsgbG4RcqWO4JL0fqix/h9w//FcPbVV8l4wQZ055GndNfY//R/8a9z6Sid3MZi/4JJ3YtwCOLjmJA+pMYeJWTZxlLT8VaZGTkQBV7ajcGsx6+Gc7ruD2LI1sykb7qCqRmDkW7SyrvAQoLC/Hc8zMw5cm/qvVzzlHT71yODr94F53u/wDJuauRmmDzZWKq7onBoqOs13/cX+eMc7fo87R729fH3Qse7OT5vce5c77+j7u4uFj9G2zZstnneYTxP1N1RsXFhb7nZ2V3PIxq26i4COVcVf8vdRXP1/7/W/R2z9p3qkr854yKi3C3UWP81G73uJuudveZ/pw7rV1zd4uROe6vtYeCPb8w5GfyMD7+nXtbWufzv1/V50tpL/k7kLJuwvi2qzMqLi74PT997l7S/2r3NWnb3P+qGncQdleGLAb1r03G1lVp6OY1y1TfQt+ZXZbezmqFAa7AtbG/0mLOsWfPHnWsPqtS1oquw5wFW1Av8QHcc72TCyKcVN2Ua9Eb08Z2Q8113h1C31bs3Ft4vI0+Jtcf6dl78K+LHDrLsvw0vnedxkWNTuLTrJFoo8bkktE3/TXHjDczyYXMk+Tifoc4H/XYZAv99evfwqlTp7SIQ/3wJdat2Atc/0f0c+Cb/aZNm6rPqiw/gM1TxyK+x3hkf3ULHhh5k8/1OfbnSeb5y5CW6fl7Ht4LCfUrOqidqvzLj7HthOeTOt0weY+rYkyu8FnE7UjF8Nl70EGbZVlUVFTxDU5wzIXPPL/ziTnT8ApGYtvhYiz923Q8/osVjhlvZpILk+7dKxYNO+oF8TMnUbThTWR+1RdZC+5FnMP+muQCRS5UZFnIeTGt0XvqQrhch7D7pSuxYdAAPJjr8qQDByrbh0Vpi4HUNNx+VQ1V2h1GLVx2FWP/4mForV+81m+Nvv2uR2HmizjUoI0KffDBB+roJPUS0/DU+JsrLthifo0uwwbh+sKVWL1Xsr69McmFid5lmbcrT4s4TSkOLH0cM9/yvAe+9j9Iaua8wgD6BUrNC8DrommXwRhy/b+w4ZV38E/HZbmKbspMjMK00e3BMuzHUPaf/6e6LB1V7EHbZeai1rG4rEo2iGnQCJfhMNZ/6MI5LWZXTHJhJF2W+/btxYkT9r8aqqa8BHuyUpE05Qg6PzwODyU00h5wFrlAkQsVnwvAYy5Bo8suAlwncMppSe7cIex4dQ9Q+ByS4mMrxqdaDUCm/ClvHo+OseORW2L3t7/gycJwWTN57NgxLWJz9a9AXJyvu/R6iP1VPdsnCSa5MNK7LPPz96mjI5R9hqXJAzBo5rcYvOxlDG33a0f+EcmFiVygyIWKXMVvT78FsW2mYHtplWxWfgYnv/0R9W5q5bxxuToJSC3Qy/gVV4xPHVqLVMn3vedit2sukpqerzjoALKz9RS0ib0F6durJrBzOHXye8/7fSfccNUluOaaa1TUMdVPYn6Nlm0vxYltH+PLqn/aar/QS9G2pf1f30xyYSRdlnFxVztnlmW5C7kTR2DKZiAxax6mdmvm2D8g/cKk4kKlMToMuhvxpzdi+Zr9+Ld6pBRFa1/DioJ4JCd3Y6Fy24tBww79kRz/HdYs/zsOaBMuykvykL3iKyROH4UuDWPO16d9/4P31eP21wRdxk1EYtF8vLBWG1v+oRhrl65GUeJEjOti//m0fGmG2U2dblKTF5zQZXmuYBWmbjjq+ewoNqTcjJZVSh/Jx/WZ+bbvv9fJhYlcoMiFirxM6ieMxdLcNFz73gg8oH7neAxY1wSTtr6KVId210ad+jfioaVvYPq128930bbs/jp+NWkJZibFnn+zlIlIRUUHHVOfNqbZAMxcm4HW6+6qeE0/MBPrmqRg7cwBjrh4C1vFE29RUQGlBtJ3P3HSX5Ay4SEkJCRoUbIymVU5IWU8hg29Hz169NCiRBWi4e/jNif9XmpJuMGio+JJdReKDx482D127FgtUikSbdck2Lgwq22j4iLQ75HqJvI3/OaKFVqkOqN+pmDjwqy2jYoLs9o2Ki6Skv6gXtfezPqZfMWFkeeyI3ZXRoC+MNxxsywdSroqZVZlkyaOru9BtdD55s7cUssmmOQiwJGzLB1KLkTkgqRiViVRzeLi4tRR36GCrItJLgL0heH79uVrEbKq6rMqiWomu4vILEtHLQx3KCa5CJE7g3nz5uDf/66YgE7WpHdVVsyqJPJNZlmyy9L6mOQiRL8z+PDDD9WRrIddlRQMvdwbuyytjUkuQvQuy3fffVeLkNWwq5KCoS8MZ5eltTHJRRC7LK2NXZUULHZZWh+TXASxy9K62FVJoWCXpfWFreJJtFY48SdjWgbirorD3XffrUXICvLz85E1ZzZmPv8C18dRUObMnYPS0lKkp6VrEftjxRM/WPGkknc8Oztb/fscP3484m3rgo0Ls9o2Ki4u9D1Skca7goVRbRsVF2a1bVRcmNW2UXFR9TG9Qk5xcXHY2w42Low8lx2xuzLCuDDcevQdwNlVSaFgl6W1MclFmD7L0jHb7ziAvgM4Z1VSKDjL0tqY5Ewgdwxy5yB3EGQ+fQdwzqqkUOmzLB2zY7iDBJbkykuQn52Ovtq+YbGxHTEqMxf5JWe1J1Aw9DsG/Q6CzCOzKit3ACcKjd5l6Zgdwx0kgCR3EvmzH0DStBIkrt6Lwy4XCrem4fJNjyFp+ALkazvoUuD0Lku5gyBzcQE4GcF5O4Y7h/8kV1qA1Qv3oHHyODx4Y1PPN8SgftwAPPb4PahXuBKr93L7mFDInYPcQXD7HXNV3wGcKHRO2zHcKfwnuYbdkLG/GAWpCaijheTbLmnYCBehFN+cZPWOUHCWpfn0BeDdu/Eujmqvc+db1JGzLK0lxIknP+DLj/fhBK7AtbG/0mIUDLlzkDsIzrI0z86dO9Wxbdu26khUGxdffDESb78DixYt1CJkBaFVPCnbg8y7hiKz7mRszR2OOK9UKZNTfGEllEpbt25F9vJlmJM1V+1PRZEl1WcaNmyICeMnaBGi2iksLMRzz8/AlCf/ilatWmlR+4nyiiffu/fNSnK3uCbFnXPkRy1WHSueVPIVF2+uWKH+raRiQlVm/Uy+4sKsto2Ki6qPSXUK/d8+3G0bFRdmtW1UXJjVtlFx4euxv2/YoP6u5s+fr0UqhPtn8hUXRp7LjmIqlgT4+hiP3JJzWjoUpTiw9HHclwmkvvY/SGpWV4tTKKRGoszIWrhwkRahSNHHTfSp30RGqFu3LsaNm4AVK97QImS2GJerGL4/5iKpqTbdpLwEe7JSkTTlCAYvm4eHEhpVxKlWuFWHOaQ6hVxgyNRvIiPdeuut+PLLQ1wzZxGBTTwp+wxLkwdg0MxvPQnuZUzt1izUGSvkhXXvIk8uKOTCQi4wiIx2ww03qOOuXbvUkczlP1eVu5A7cQSmbAYSs+YxwRmMde8ij12VFE4yy3Ly5HTVZckNks3nN1+dK1iFqRuOej47ig0pN6Ol17jd9Zn5qDpqR8Fjl2VkyRRvGTdhVyWFy80336y6LLlBsvn8Jrk6CY+goMbxuoqP6ovEKRTssowcGSeRNx8ZNyEKl3bt2uHKK1vh3Xff1SJkFvY8WoDcUcidBReRhp8+TqKPmxCFy5Ahf8S8eXPYZWkyJjmL4IysyJBxErmgkHETonCSLkvBLktzhVbxxA8Zq2Nlk+CcPXsWyWNG465Bg9GvXz8tSkZySjUKsg+pqtPsimYYMWKEFrGHKK944h8rnlTyFRfejz377LPuLl1uDXvbwcaFWW0bFRdjkpPVv683s36mYOPCrLaNiguz2jYqLgL9nuzsbPV+mJuTo0WqM+pn8hUXRp7LjthdaSF9+/ZVXZZyx0HGknGRDX9fr8ZJiCKFGySbj0nOQvQZWZ9++qkWIaPo4yLcAZwiiRskm49JzmLkTkPuODgjy1jZ2dncHJVMkZw8Wm2QzHWw5mCSsxj9ToMzsoyjb456U6ebtAhR5HAdrLmY5CxG30xV7jzIGPrmqB07dlRHokiSdbBdu3Rj6T6TMMlZUPdu3dWdh9yBUO29/vrrqj4oN6Yls3Tq1EmV7uM62MhjkrOgtm3bquOGDRvUkUKn7zgwbNgwLUIUeVdddZU6cmeCyGOSsyC54+DOBMbQ/w1ZxovMJJupcmcCczDJWZTcecgdCNfX1A7LeJFVcGcCc4StrJc3lvkKDst81R7LeJHV2KXMF8t6+cGyXpV8xYW/75k/f74qQ3XmzBn1tVFtBxsXZrVdm7heJk0XybarMiouzGrbqLgwq22j4iLUc+llvo4fP66+DvU83nzFhZHnsiN2V1oYuzdCJzNTZZuT0aOTtQiR+RITE9VRX9ZC4cckZ2FS5ktKAq1bt06LUKDy8/epo147kMgKZM2cTCqTZS0UGUxyFicVUJYvX8Y1c0FauHCRejNhGS+yGk4qiywmOYvTuze4Zi5w8ubBtXFkVbKcRQqxv/3221qEwolJzuKke2Po0Pu5Zi4I+psH18aRFclyFinEPn16hppFTeHFJGcDsoRA7kwOHTqkRcgXedOQNw9ZeMu1cWRVPXv2VMcvvvhCHSl8mORsQGZZSvfG3r17tQj5or9p6G8iRFYUFxenJpVtfWerFqFwYZKzCX2fOU5AuTB505A3D3kTIbIy7jMXGWGreMIKJ8Y6duwYJk76C5JHj1F3dvRz+r9RyoSHkJCQoEWJrMnKVY1Y8cQPVjyp5Csugv2epKQ/uAcPHqx9Vcmon8lXXIS7DSPiUiFG/vb0CjHezPiZhFFxYVbbRsWFWW0bFRdGnSv14YerVTXSGXV+YeS57IjdlTbS47YeagIK96T6OansLsWYE2+/gxNOyDZkBjCrGoUXk5yNyJ5UMgFl48aNWoR08iYhbxadO3fWIkTWJ8UKZAw5Oztbi5DRmORsRPakkgkoUpORE1CqkzcJebNghROyG5mAsn79W6yAEiYhJLmTyM+8E7Gx45Fbck6LUaTcc8896sgCr5XkzUHeJOTNgshuOne+RR1ZASU8gkxy5SjLX4a0zD3a1xRpegWUzMxZWoT0Nwf9zYLITmQMWYoXSBED7hpuvOCSXNk+LEqbh0LtSzKHTDeW8addu3ZpkeglbwqscEJ2pxcv2LRpkzqScYJIcieRv2gaMnEPUoe11mJkBlknxy14KuhvCrJbA5FdSfECbsETHgEmOb2bEkidNhpdm9TR4mSWe++9V23BE+3VEuRNgVvqkBPoW/Cwh8ZYgVU8KduDzLtGYlOfv2FVahsczByEpMw4ZO1+EUlNf57wpOKJL6yEYoxTp05hQsp4S1ZLiJTCwkI89/wMPDrpMcTHx2tRIvua9OgkxLeJx4gRI7SIOaKs4sn37n2zktwt+sx27zv1k+frU56ve7tbtBjnzvn6PxVP8cKKJ5V8xUVtz6VX+MjNydEi1dX2/FUZdS4j45MnT1bVIqry9XxhZNs1CXdcmNW2UXFhVttGxUW42sjxvJblNf3mihVapLpgzy9q+zPZXYzcdfn+GIcVW5Zo3ZT3I6F+CCsOKGz0cahPPvlEHaOJdNNKd21q6iNahMj+unTpoo7vv/++OlLtxbhcxfD9MQNXf7oRhdiDzKTrtMR3DZIyP/N8ay5SOiZgVO7/VZyJIk7GoWQ5QU5uTtRNPdbLIPXp00cdiZxAlgjJTOFVq/+XBR8M4ufWrD4SUjd5Jb7PkZt6reexJGTtzsfipBYVTyVTyHjcd999G1W17+TFL28CXDZATqT30LDggzHY/2hzspwgLu5qvPjii1rE+TZs2KCOevUXIieRHpquXbqpgg9cHF57THIOcGfSnVEz9Vhe9IsWLVRvAtK1Q+REvXv3VgUf8vLe0yIUqhCSnN6FObfG5QMUefruBNGwOFwWf8uLX94EiJxK351g4cJFWoRCxTs5B5DdCWSWocw2dHolc+nC4eJvigYPP/wwF4cbgEnOIWSWodzNLVmyRIs4j7zY5S5OKkMQOZ1evi+axtvDIbCKJ0GSpQasbBJ5kgQWLnoZGc9Mc+SdTsa0DHVMT0tXRyKnM6uqT5RVPAkeK55U8hUXRrdx5swZ9W8vlUCEUecXRp0r1HheXp763eQogj2PCLVtb2bFhVltGxUXZrVtVFxEsm2p6jN48GD1ebDnEbVp2wnYXekg+r5UThybky4b6bqRLhyiaCLj7RybCx2TnMPoa8ecNDYnL255kctAPFG00cfbOTYXGiY5h9HLAjlpGx7exVE0kx4a/W5OxugoOExyDiR3c3Llt3nzZi1iX/Ki5l0cRTv9bk7q1FJwmOQcSO7m5Mpvx87tth6bk+om8qLmXRxFO7mbmz79Wc/r+SDH5oLEJOdQcuV36aWX2XpsTqqbyIuad3FE0Vmn1ghMcg4lV35S01LG5ux45Sd3cVLdpH37DryLI9LodWpzc3O1CPnDJOdgHTp0sG3FhNWrV6vqJgPvHKhFiEgWhEtZO+5QEDgmOQeTmpZ6/Ts7XfnJfnFpaY+rDWFZo5KoukceeURdAMqFIPkXtrJe3ljmyzxz5s6By+VCxjMZKvFZnYwjyqSZOVlz0aBBAy1KRLqVK1diw9/XY+bzL6BJkyZa1Dgs6+UHy3pV8hUXkWr74MGD6v9k/vz56utgzyNCbdubv3hBQYH6WbOzs9XXRp1fGHUus+LCrLaNiguz2jYqLsxqW48fP348oBJ+wqi27YrdlVEgLi5OLRCfPj3D0ksKZIwhIyNDrQcaNGiQFiUib7JMKCtrrm0nlkUSk1yUGD58uEoe6enWreAvYwwyfijrgWR2KBH5JsuEZGLZ5MmP4+zZs1qUvDHJRQlJGk8++aRKIla88jt27Nj5ySZcMkDkn7ympedDJqE4obpRuDDJRZGePXupJCJ7zlmtruUbK95Qd5oTJ07UIkTkjwxFjBs3AatW/6/jdh4xCpNclJEkIpVQnnnmGS1iPlnesG/fXnWnKWMNRBS4lJQU9ZoeNWok187VgEkuykgS+eOQP2L9+rewfPlyLWoeufpMSRmPrl26qTtNIgqOdFs+MPYB1W2ZlZWlRUnHJBeFEhISVLeljIGZ2cUhV51y9SndlHfddZcWJaJgtWrVSs2gnjdvDmdbemGSi1LSNSjJRZKMVBgxw9NPP61dfc7hom+iWpIZ1FLyS2ZbOmUvSSOEreIJK5xYn7wQ0p9IU0WQxySPiWg1lK1btyJ7+TIM89xR9nBSdQUiE8ks5RnPzUCjRo0waeKkkF/TrHjiByueVPIVF2a1XTW+Zcvm89VQfD1fGNl2Xl5etWoNwsjz+xLuNsIdF2a1bVRcmNW2UXFhVtuBxPXX19ixY9XXRrVhV+yujHIy2UOvhrJu3TotGj5y9zhkyN2qW0W6TInIWLLOVKqhyOSyl156SYtGLyY5wgMPPHB+rU04B60lwb04+0U1FiiLWFnVhCg8kpKSInrxamVMcqTIWhsZm5O7rHBsyyMJ7t57/6g+f/31N7gejijM5OJVEp1cvEbzHV3ASa68ZA+y0/urSSXy0WbUAuwpYb00p5C7Kpl8IksLZN2akS8KuTv8/e87qc8fe/Qx7hFHFCGS6O4aNFjd0clrOhoXiweW5Mr2YPbwVOyIexaFrmIc3v0qBhdnYtDwBcgvK9eeRHYnM7GmTZt2vpsjLS2t1i8KWXCuj8Ft3LgpLHtfEZFv/fr187yun1WvadlwNdqWFwSQ5H5A0aoXkfnVbRg6sA3qeyIxTbtj4uP3oF7heuw4eKbiaeQYcvX3yitL1DYeffv2CWmcTl5Ich5ZcC5Jc9asWRyDIzLJ0KFDsWLFShQWfqaGDd5+e4v2iPP5T3LlXyFvzV7UG3gbEhrqT49Bw25PYb9rE1ITJO2R08isy3/84wPEx1+r7sRkt+6PPvpIe9Q3SW7SLSLr7+QF9dZb61WyY4IjMpfMuszJyUXnzrfgz38egYxpGVFRHSWAJHca37tO46JGJ/Fp1ki0UWNyrdE3/TXkc0zO0WTsTBKWXAEe/foo+ve/A127dlExmZwiJcEkqclVoXRL3n333WrsbcWKN5A8eozqnmzXrp12NiIym0z4kiEJeU0LuYCV1/SMGTPOv6ZPnTqlHnMK/xVPSnIxquN4bEYz9J74Ip4ZfzOa4ii2Tx2D+3f3Qu6q8UioXz1XysQUX1gJxb4OHTrkuTsrxI6dO/Ddd99q0UqJt9+B6667DldddVVEq6cQUWj01/RHH3/kSXAHVUwuUJ9w0hpWtST8Qr7OcY9s0dx9zZgc95GftJjHTweXuPu36OxO2/adFqnEiieVfMWFWW0HGxfej505c8Z98OBB97JXX3UfP35ci1YK988UbFyY1bZRcWFW20bFhVltGxUXZrUdbFwE8z3yms7NydG+coYYfUlAzR/jkXuqAS6vB1zUOhaXVblhi2nQCJfhMNZ/6MI5LUbRQ8bYZMNG6dLkmjciZ5DXtNOKpce4XMXw/TEXSb/9jecX92S5GtVD7K/qBbgOgYiIKLL856eYX6Nl20txYtvH+LLKkrjyUyfxLS5F25a/ZpIjIiJLCiA/NUGXcRORWDQfL6x1QeW5sgNYu3Q1ihInYlwXLu4lIiJrCugmLKbZAMxcm4HW6+5CSxmrix+GdU1SsHbmADTjbRwREVlUgCkqBvXjeiF18W5trG43Fqf2QpzX0gEiIiIrYZYiIiLHYpIjIiLH8l/xJASyxo6VTYiI7Om2Hj20zxxALQk3GCueVPIVF2a1HWxcmNW2UXFhVttGxYVZbRsVF2a1bVRcmNV2sHFh5LnsiN2VRETkWExyRETkWExyRETkWExyRETkWExyRETkWExyRETkWExyRETkWExyRETkWGGreOKNFVCIiOyBFU/8YMWTSr7iwqy2g40Ls9o2Ki7MatuouDCrbaPiwqy2jYoLs9oONi6MPJcdsbuSiIgci0mOiIgci0mOiIgci0mOiIgci0mOiIgci0mOiIgci0mOiIgci0mOiIgci0mOiIgcK2xlvVjGi4jInljWyw+W9arkKy7MajvYuDCrbaPiwqy2jYoLs9o2Ki7MatuouDCr7WDjwshz2RG7K4mIyLGY5IiIyLECTHJnUZL/GtL7tlbjbbGxHTEqcwuKysq1x4mIiKwngCRXjrL8BRieNBvHx27BYVcxXIXzcO2m8RgwfSdKtWcRERFZTQBJ7gwO7liPQnRE35uaVXxD/Tbo2qclTmevwjsl59SziIiIrIZjckRE5FgBJLlLcHXXOxCP3dj4/lGoUbiy/dix6TDqJfZEx8vqqGcRERFZTQBJLgb1E5Ix56k4bEi5GS1l4kn8ncj86h689NwANOO9IBERWVQAFU/O4mjuJPSY/CMey30Ow1s3BMqPYvvUMbh/dy/krhqPhPrVM53MwPSFlVCIiKzNURVPpDqJ749x7pyDb7vTrmnuviZtm/tfav14hZ8OLnH3b9HWPTLHpUUqyffWxMiV90ady6y4MKvtYOPCrLaNiguz2jYqLsxq26i4MKtto+LCrLaDjQsjz2VHMS5ZEuDzYy6SGpzCN6eBi5o0xCVaYhQxDRrhMpzA3i+/A+dXEhGRFfkfUWsSi2sba59XUX7qJL5FY3S48lJw6gkREVmR/yRX5zrcM3UQfty0Gm/kl1TMriw/ip3Zq1EQPwoP9myunkZERGQ1AcyNrItmSU9j7aTLseO+DhWzK1t2x7M/DUHu0rE/m3RCRERkFQFmqIaI65GCxfv1sboD2JhxHxKa1tUeJyIish7ehhERkWMxyRERkWMxyRERkWMFUPEkeFLxhJVNiIjsyVEVT9SScIOx4kklX3FhVtvBxoVZbRsVF2a1bVRcmNW2UXFhVttGxYVZbQcbF0aey47YXUlERI7FJEdERI7FJEdERI7FJEdERI7FJEdERI7FJEdERI7FJEdERI7FJEdERI7FiidERFSNkyqehCXJERERWQG7K4mIyLGY5IiIyLGY5IiIyLGY5IiIyKGA/w8gIvP1oN79nAAAAABJRU5ErkJggg=="></p>
</div>

<div class="specification">
<p>Another wave travels in the medium. The graph shows the variation with time <em>t</em> of the&nbsp;displacement of each wave at the position of P.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
</div>

<div class="specification">
<p>A standing sound wave is established in a tube that is closed at one end and open at&nbsp;the other end. The period of the wave is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>. The diagram represents the standing wave&nbsp;at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math> and at&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mi>T</mi><mn>8</mn></mfrac></math>. The wavelength of the wave is 1.20&thinsp;m. Positive displacements&nbsp;mean displacements to the right.</p>
<p style="text-align: left;"><img 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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the wavelength of the wave.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine, for particle P, the magnitude and direction of the acceleration at <em>t</em> = 2.0 m s.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the phase difference between the two waves.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify a time at which the displacement of P is zero.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the amplitude of the resultant wave.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the length of the tube.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A particle in the tube has its equilibrium position at the open end of the tube.<br>State and explain the direction of the velocity of this particle at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mi>T</mi><mn>8</mn></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw on the diagram the standing wave at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mi>T</mi><mn>4</mn></mfrac></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo></math>«s» or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>250</mn><mo> </mo></math>«Hz» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mn>340</mn><mo>×</mo><mn>4</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>=</mo><mn>1</mn><mo>.</mo><mn>36</mn><mo>≈</mo><mn>1</mn><mo>.</mo><mn>4</mn><mo> </mo></math>«m» ✓</p>
<p> </p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong>.<br>Award <strong>[2]</strong> for a bald correct answer.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϖ</mi><mo>=</mo><mo>«</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow><mi>T</mi></mfrac><mo>=</mo><mo>»</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow><mrow><mn>4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow></mfrac></math>  <em><strong>OR  </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>57</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></math> «s<sup>−1</sup>» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>a</mtext><mo>=</mo><mo>«</mo><msup><mi>ϖ</mi><mn>2</mn></msup><msub><mi>x</mi><mn>0</mn></msub><mo>=</mo><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>57</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow></mfenced><mn>2</mn></msup><mo>×</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo>=</mo><mn>14</mn><mo>.</mo><mn>8</mn><mo>≈</mo><mo>»</mo><mn>15</mn></math> «ms<sup>−2</sup>» ✓</p>
<p>«opposite to displacement so» to the right ✓</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«±» <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi mathvariant="normal">π</mi><mn>2</mn></mfrac><mo>/</mo><mn>90</mn><mo>°</mo></math>  <em><strong>OR</strong></em>  <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mi mathvariant="normal">π</mi></mrow><mn>2</mn></mfrac><mo>/</mo><mn>270</mn><mo>°</mo></math> ✓</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1.5 «ms» ✓</p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>8.0 <em><strong>OR</strong> </em>8.5 «μm» ✓</p>
<p><em><br>From the graph on the paper, value is 8.0. From the calculated correct trig functions, value is 8.49.</em></p>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>L</em> = «<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mfrac><mn>3</mn><mn>4</mn></mfrac><mi>λ</mi><mo>=</mo></mstyle></math>» 0.90 «m» ✓</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>to the right ✓<br><br></p>
<p>displacement is getting less negative</p>
<p><em><strong>OR</strong></em></p>
<p>change of displacement is positive ✓</p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>horizontal line drawn at the equilibrium position ✓</p>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>A pipe is open at both ends. A first-harmonic standing wave is set up in the pipe.&nbsp;The diagram shows the variation of displacement of air molecules in the pipe with&nbsp;distance along the pipe at time <em>t</em> = 0. The frequency of the first harmonic is <em>f</em>.</p>
<p><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>A transmitter of electromagnetic waves is next to a long straight vertical wall that acts&nbsp;as a plane mirror to the waves. An observer on a boat detects the waves both directly&nbsp;and as an image from the other side of the wall. The diagram shows one ray from the&nbsp;transmitter reflected at the wall and the position of the image.</p>
<p><img 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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch, on the diagram, the variation of displacement of the air molecules with distance along the pipe when <em>t</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{{4f}}">
  <mfrac>
    <mn>3</mn>
    <mrow>
      <mn>4</mn>
      <mi>f</mi>
    </mrow>
  </mfrac>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An air molecule is situated at point X in the pipe at <em>t</em> = 0. Describe the motion of this air molecule during one complete cycle of the standing wave beginning from <em>t</em> = 0.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The speed of sound <em>c</em> for longitudinal waves in air is given by</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c = \sqrt {\frac{K}{\rho }} ">
  <mi>c</mi>
  <mo>=</mo>
  <msqrt>
    <mfrac>
      <mi>K</mi>
      <mi>ρ</mi>
    </mfrac>
  </msqrt>
</math></span></p>
<p>where <em>ρ</em> is the density of the air and <em>K</em> is a constant.</p>
<p>A student measures <em>f</em> to be 120 Hz when the length of the pipe is 1.4 m. The density of the air in the pipe is 1.3 kg m<sup>–3</sup>. Determine the value of <em>K</em> for air. State your answer with the appropriate fundamental (SI) unit.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Demonstrate, using a second ray, that the image appears to come from the position indicated.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the observer detects a series of increases and decreases in the intensity of the received signal as the boat moves along the line XY.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>horizontal line shown in centre of pipe ✔</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«air molecule» moves to the right and then back to the left ✔</p>
<p>returns to X/original position ✔</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>wavelength = 2 × 1.4 «= 2.8 m» ✔</p>
<p><em>c</em> = «<em>f λ</em> =» 120 × 2.8 «= 340 m s<sup>−1</sup>» ✔</p>
<p><em>K</em> = «<em>ρc</em><sup>2</sup> = 1.3 × 340<sup>2</sup> =» 1.5 × 10<sup>5</sup> ✔</p>
<p>kg m<sup>–1 </sup>s<sup>–2</sup> ✔</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>construction showing formation of image ✔</p>
<p><em>Another straight line/ray from image through the wall with line/ray from intersection at wall back to transmitter. Reflected ray must intersect boat.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>interference pattern is observed</p>
<p><em><strong>OR</strong></em></p>
<p>interference/superposition mentioned ✔</p>
<p><br>maximum when two waves occur in phase/path difference is nλ</p>
<p><em><strong>OR</strong></em></p>
<p>minimum when two waves occur 180° out of phase/path difference is (n + ½)λ ✔</p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A student is investigating a method to measure the mass of a wooden block by timing the period of its oscillations on a spring.</p>
</div>

<div class="specification">
<p>A 0.52 kg mass performs simple harmonic motion with a period of 0.86 s when attached to the spring. A wooden block attached to the same spring oscillates with a period&nbsp;of 0.74 s.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>With the block stationary a longitudinal wave is made to travel through the original spring from left to right. The diagram shows the variation with distance <em>x</em> of the displacement <em>y</em> of the coils of the spring at an instant of time.</p>
<p style="text-align: center;"><img 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KEdPALnYEr38nSMqtwA3dcUzouCEDRu3Fh3Rv62wiNAQSsoXiL3e17hh0IRAOKFtJ0HhnzaH998vAhf9XDAgMcvADxF+s04RG5dhYn/uYKWH3+NLo10VZWD+8d/R5gGW+us2F3YFFvEb+GFO8YP12Sap56vfO5JKB89ehT79+9XBBtQ5mLw4MFFfq2FEF/K7/l1xUKAQmxRsGQaK9u3b1dpPPmnHj58OLy8vHgAARVkKtgNM0V6eZvtn92PySjyrMqfjLUcsZydePDSFLUYTIN4MWfKzs5m4eHhCgwGDx6suE5ISGC3b99m9I6ujx07xubPn6/IExQUpHhnTh55XdJAgMYE9T+NURoPNC5ofNA4oXd0TWOJxhHloWt6x1PFQ8B0h1lYNlLOn8LJmPNISnsOyORwe60DundpidoGOfvPQ9btS0h48Fz357JGXTRp0hj1Zdpn6OY8zELL1M8++0zBM0Xn6Nq1q07+09LSsGbNGsyYMQM8Fp5OqKzuZUREBIYOHQp9w2wJ4d8IiO+++46rzaxuRJTSINN9l/JYTvp9lpycXPIvJZ3l5OtbUyaLCfFWzB5UZ+Xqs3QwyLqxCWHxLFMLbXPNpGkW1KFDB7Zy5UqDZztnz54tKqsvQjyf5SJAY4TGCo0ZQxLNoo0ta0g9PK/0EDCBPiCXZSZsY/NGdNCg7hAE63gWnqyvyuMle3h6NfNvKWOQvcn85/7Ifg0PZ+G/rmUhkwaxFgCT9Z/FNvz6A5s13JMBXdgXe+8yTXLaHEKafmxUD/2AjE20vBWEvLE0eDnpIyAIWepvYxPRoPFmqJA3tj5ervwR0K4rKGUGXvQ6Pwl/BE/GzG1V4D1iIrq3bwIHJVvpgnzN0MJeX2s/hhe3zmHHlTcx/+QvmNa5TrHr0/feRbcGH6DLwuuwWTEDX7/dFJnH+uKnX/9CkI8f5CXqLeKyTC5IxdGtWzesXLmySNVhTEVk9UFLYD8/P0VxQW1iDC1eRpoIkJoiLCxM0c9irHyEsUHjLiEhgQe9lWZ3m5Yr0d+J5HDmDzD55L0sVdN01uAK7rId490ZWoSwGA2T75cxIawFWjD/8FuMsVss3L+F1rxlOZNOTU01+eyXZljEM20S8WQ9CERGRir6lTYDTZWEWTmNQ56sGwF9p7favwwmicyiTL4SqlSvBqQl4eYDdTO7l3hwMwlpkMGxZlWAPcdTMvlzqAqD9iaVqzPyOjg4GJ6enhg7dqyRFEoWoxlWZGSkYlOJTLN4snwEaLXl6+ur6FdTmlzSuKPxR+OQJytHQPw36Cm79uvHrGXLT1nYhVSmYfJrYBW5LPXATOYOMt9bwH4/cYndos3IW5fYyT+XFOiq3WeyA6lpLGnvAtZfJmPusw6zxxpqKauZNM10SYcsRreogd2iR2SSRaZX3OSqCBKLvKD+o36k/iyLJOxl8JVXWaArHZom2DhkLP/xXyzkbWfFko4EY4k/2US240Gu/q3Oz2AXwiayDrKStGQdJrKwCxks//EBNlUOhpYfs1+vPdVIuyyEtKCSoCVsWSX6cdNHYMOGDWVVBadrBgSo/6gfy/JjK6hSymrCYAaYeBWlICDeTprdxs5P38XA1bGArD36D3kNddWVKAaFzxKWLvl4lnIBJ0/G4HxSGl5UrYPmHl7o0qUN5NVtgWfXcfTATdR6oyM85HbFm4tCcQBlYSc9depUpKen46efflKqyfSXdAqNlsm3b9/mdrGmh7fMKZKaw9nZWaHm8PHxKdP6xo0bB0dHRyxevLhM6+HEywcB8UL64U5MaD4Qvw37GadXv48WJEAlkkwtpOPi4tCuXTuz7arTB4ES//FJZEAZwIa5PubEEu1fuLm54dixY6UeojKgCTyrRBAQL6SfRCPYvTd++/QkLs/oDN0BrbS0utDB0t6mAVg6pQMebvk35u9O0ZKZHuvnYMnUQnrIkCEKvxuCGZQOBk3ySvjxcVMrk8BpNiLl0W9k4kf+P7Zt22a2dvKKzIRAKeoQPV5nsoSw8axlh+ls580sjYdKSiWSG8eWt5Mx2fgd7AHLYnHL+5bUa6vout3Z+B13SyVrSp20cGjF3CZP5N+BNp94shwEqL+o38yZaFzSeOeHXMyJunnqEj+TplnwpCCEbPgTsTCFTvo5kn4OxvTLnTDtX+/Bs7bxkVlMOZM29yxa+EYLszK+lBUQkfZ/8rNRXgdN+Gxa2mPDWO5MIKTjsaJDN0zS4Ga0iCnZROxIWoYB9fURuLcRMbonhh4JwMnL09C5mvHHCE0lpIUfHvmErlPH/LEVzanfLOozfmEUAuW5j0BOu8gXNf+gG9V1ki0kXkibvGnZSNoyBX0DH+GzfcvxUSc5qhspp00lpMtrFi1AK8ymuW5aQESa/6XQT3w2Lc2xIYYrCQrp57h9YBn+9fF8bL2SBZmIyCymENJS+OFRB5fnDE3MAKtIZRcsWIDr16+XuXmmLkwF07+zZ8+ibdu2urLydxaCgMmENHt2F2cO7MPBI3/j/AM3BC4dh0YnwnG+cV8M8mwA/T05PUX8imFoO2mvDgjdMX7HAawZ4KQjj2nspOmHl5GRUe5mcOWtctEJNH8JKaka+AfdygakKfYn89NOsJBB7koWGeSa9A7bO8mTQdaPzd5/2wTHxQ3nVKx1h9R2zPkpRMPHgLlKCKcLzVWfrnrKyxJJF0/8nfEIiD95wh7g4KIpCIp+DSFHLuLwYu/Cz1hD9A7+BsGt/sKcyRsRk00y3LLSzp070aFDB8kcEPjyyy8VkTksC8WKwS3pgs1lP18aohQViMYtjV+eLB8B8UI68wIiw07AceQY+HdrgppKm3yV5d4ImNAHuPA34m7kWBxa5ONZKj88As/b2xunT58GqT54kg4C1B/ULwMGDJAMUzRu6cPBk+UjIF5IP83AvRSgTgs56igJ6AJoKsO+NpmsPUZWTr5FoUVHwCl6s5R+eGT+R/ETDx8+bFFYWjuz1B/UL+VhnqkNWxq39OGgccyTZSMgXkjXksO1jQz3z1xFsrpGgz3CuaOnAJk7mjtVtyikyNY0MDBQUj88AnDw4MGK4LW0UcVT+SNA/UDBhKlfpJTog0Hjd/fu3VJii/NiBALihbSdB4Z82h/4ZRG++vEobpATfjxF+s04RK6cjon/uYKWo95Bl0b623cY0Q6TFsnJycHEiRMxfPhwk9I1BbE33nhDoW+MiYkxBTlOQyQC1A+k/6V+kVoaM2aM4gNC45kny0XANCZ4uXdwYO5HGDJnD7JUsJCh5Yj52LDyE3Spb6CQZtlIOXMIew4ewanzj+ESOAdfNDqNH887YdggT9TXIxSLsXbSgrlbdnY2atSoodIiKdyQrjE+Pr5c7XGlgIMUeCA3oRQhRUp7FwIuJJzt7Oz4CUQBEAv9bxohTY1nqYgP34nYx0+Qlv4cYPeRmOKFyXOGobVMn+PgSgiyR/jr208wMmgrriket4B/+H4sq/kdXPr+hrazQ/HzrD6QlyKojRXSZBtNafr06UpMSedScJlaXsfUpYNE+XIi2EZL+eCI1Mdy+faghdRuvPVeccn8zHgWNqEbk8mnsQOP8xQvci+uZt0AJus5l+1PflacudQrIXxWMzYo5BC7eXhhceDZl7fY3mBvBnizeSfTS6VkjJ00RdGwBG9iZDNdltFhSgWXZ1DgT/0g5STYTJdldBgpt98aeBOvkyY76Xkfw39NJvp/1h3NqhaYeNg28cGCDcHocHoWhnz8MxJfqu8qavuKpSMucg8uOw7GOP+ucKqppCap7Iy3A0bBB/HYG3cHedpIiHh+5swZRWkp6hiVm+Xv74+tW7cqP+LXZkaA8Kd+kHISxrEwrqXMK+dNMwLihbRgJ/3hbCyd1g/NC70h2ciao7v/TCyb3x9Z2/fi2PXnmjko8TQHGfcygDqNIa+jJKAL89na10YjpCMl67kiAGKJ4iIfkDnV/PnzJamLVm4aucNcu3at4jiy8nN+bR4ESNVB+FM/SDnRngqNZ262KeVe0s2beCEt2Em3booGJeykq6NB48YAHiItM1c3J0Vv7eHk6gzcv4SryWQpopzykHbuL+xDS3RvXh8GarqVCWm8po0WMqfq0aOHxvdSekjOc8iqgFt5lE+vCFYdluDEiMYzjWtu5VE+Y0VsreKFdJ0m8PCU4VpUTEmVhlF20rXQdsgHGITfMOur9Th5Iw15yENO+g3ER36PLyauRkrLARjaRa4x+KwYQMgVKKVWrVqJIWO2srTUppBJPJkfAcKdXNhaQuIqD0voJR08ilesP2UJof9gMshZhzGL2C/7T7CYmBh2+sh2tmbqYNYCMuYevJ+l5htS0zOWvH8u6ylTaDQUG3m0maf4a/l/bMmJe3qF6TJ043DlypUsMDDQEEbLNS/fFCof+C1lc1kZHRrXNL55sjwETGOCl3sXR/4TjMCgn3FF5YPgDO/JIfh+rhFmeMjHs5QLOHkyBueT0vACMjR0a4NO3TvBtXYVlVq03RhqgtexY0fMmzcPPj4+2khK6jm3gy2f7pC6Hb0mVKKiojBz5kycOnVK02v+TMIImEZIKxpIQjUR8Zeu4W7Gc9jWbIBXm7vBzaW+0ZFVxOJmiJAWnKXfvn0bjRV6dLG1m6c8+Q5u0qSJJA9TmAcB89dCh4lu3bpV7j7GDWm5pY5vQ9porXlLmk8Y3VJbVJe7o5Pc3WgKKgVzs5CSlITkzJcqjwtuKsG+aSu41qum4Z1xj2iGQf4XLElAU0v79OmjmCFJ8cSbcT0h/VJhYWGKFZf0OS3mkMY1jW8a55Y2xotbUTGvTCSkGXKz7iIx4T7UvQSw7PtIiEtHi5Hvo7OjfvYYLOsc/jtxDMauP6ulV+gE4kFs8HPW8t7wx3v27FEIPMNLlm+J1q1bK7yd0UyJ//jKvi8IZ/IuR7hbWqIPOo1zPz8/S2O9QvNrAiGdh/S/VmLMyFn485qq544iZCla+PvvF93qvsjGpU2zMXb9PXTwn4Px77SGYxV1274qqN/OdFG7SbdLNq90vNfSEp8hmbfHLHXFRSiRTTc5DluxYoXkzwGYt1elXZt4IZ1/BX98tRh/3n8d/jN7ocaxDfghxgXjp3YBDm7FDwdfQfDvQehbX79ZNJCKyycvAPKRmLtsOnzr6FvOeKAF0zs3NzfjiZRjSZoh/fXXX3yGZIY+IJwJb0tMwvim04cUvYUny0BAvJ106lWcOpECx5HTEDJnJoID3gKy6qHjiFlY/ecvWDHoNiK2x+GhvqfCUQO1G9UGKtvBrpp49vTpBvIdTU7bpejxTh/+aYYUEhLCDyvoA5bIPIRzu3btRFIpn+I0vmmcW+KKsXwQk0at4qVg7gvkZAmRWaqiQTMXOCMJCXeyYCNrgwHDOuPK6i3Yf0PfY+F18WbAZxiRFYWIfUl4prdwNx5QOpjQuXNn4wmUc0lhhiSsCMqZHautXohyIhwOscSG0jjnB6Asq+fEqzsc6qOpM7DjWgrSmA3qNWyCVniAhLsZYKiFylWrAriO+2kvgVe1WGPkJWLL5IXY/UQIsfUU9+ucx5Z3XbC2fX8Mea0uVL8mdvAInIMp3euLRpt8MFCYrMWLF4umVV4EaIZEUTjOnTsHSzimXF44ia2X8CWcLXXFRe2nswBDhw5V+HyRUrgvsX1jzeXFC+marfH2mG6Yu2whgls7YnFAK7zVJh3fbPkNO13a4fofxwBZdzjXJ2GtLeXg/vHfEXa25MZjVuwubIpVL+eO8cM1meap5yv9/tKlSwofGK6urqVnlnCO7t274+jRo5L3yiZhCEtljfAlnC050UYz+Xyhcc/10pbRk6oTVKN4rotuExdiSf+nWL8zAek13kDAf4LR4fAMDHrzHUza8gw9p30IH2cdQrqSJz4/kwnGGBh7iYdxkQj/4yiScvILn9Hzwr+cJBzeNAVvyauZxAse6ecsxQeDru55/fXXFRYq3ImOLpSMfydYABHOlp5ovHO9tAX1oslOsr98zG7fSmUvFQRfsPRrf7G9f2xje3cHE5YAACAASURBVP+6wTIN8tuRyWJCyLH/eBaeXEBNmcf8W7+yEQBrERJTWJfyW9VrfXx3DB482Gqc51N7z549qwoCvzMJAoQr4WsNzvMpWITUgxWYpNOshIhRx8LzErdg8vzdeKLvx8i2HQKXTkR3rYdZcvFg5xS4D1yOdL1oNsOQsCiEj2qppqtWLVzasXAh/JGlHQVXbWXxHR0Rb9OmDVd5FENisis6ZXjhwgWL3rsQwOBHxAUkLOO/cTrpnPs4HhYGvY9+yGphuM59ucpo4PsZ1n75FNuTs5F68SB2xcrgPbwTmtRQ18jYQe41EAHvNtcpoPWBX9BHW8tJPdq5pxNlUo8Wok/fSC0P6aP79esnNbaM4kfQS9+8eZOfUjUKQfMWMmomXbYsPkX8imFoO6MldiQtwwC9D8GU5Kq0mTQ5ynny5IlkA86WbJHuJ4mJiSBzPKlGOdfNvXTfCt4GycTR0jeYBZQpQK2DgwN3zCUAIuH/6tNUCbBaE56f7wHLXCFKQOvTELIX9fLy0ierReQRBAi3lzZtdwl4OjubzleMaTk0nBqNe24vbThu5VHCOHVHCU4ZcjOu4ERkNI6diUfCvWzYOjZHxy490du3i97+n0uQLcMHgn00zaatKXF7adP3ZlJSksXbR6ujQg6i6HwA/Q64vbQ6OtK6N4GQZshN2Y+5/zcWcw7eVmnd+uX/hqznXGz7OQi95VoOsqiUMN8N6aMpWYs+WkCO7Hhpg4sn0yFA/jos3T5aHQ1BL83tpdWRkd69eHUHu40/Z3yOOadfQ/Cvf+Nm5kswlo+Xmcm4uH8F/O4swpCPfy4Z/7Ccsbh27ZrCj0E5s2Hy6smOl/xL8GQ6BAhPa7CPVkfE29sb9DvgSdoIiBfSj84hautlyAMnY+p7HdFERpNzG1SWydG6dwCC/+mDrO1/IvqKuqfp8gWGdust2V+HNvQEPx60iciTeAQEHAVcxVOUDgUa//Q74EnaCIhXd1SqgupVgMr2dqim7vYZVWHvWAtACl68NNBTEnuC68cisXf/cZy6kY58W0c0bdsOnbz7wdezAcQwLpweI49g1pYEPx6k8hA2Eq2tjeZsz40bN6xOHy3gRzb15MeD+5cWEJHmfzGyrqBFju0xYkp/hK7fiC0jXseHr9VCgaxmyE0/gz82H4Rs0DT0drPTHwF2D0e+DkD/r/egpDePdhgTtgmrR7VGdf0pquSkwyuUrFWIeXp64vLlyypt5jfGIRATEwPC0xqTMP7p9yBcW2M7Lb1N4tUdLBs51ZzhlfITxrbpgN4TZiFkyRKEzB4Pnw59MOnPPHjJk7Hnu2+xZMkSLFmyAlviM3Tgloe0g99j/Nd/wW1CKE4mpSInn4G9zETyhZ2YN+gJ1n8yH5sTs3XQ0P2KZplkBWGtifwdb9u2zVqbZ9Z2EY6W6j9aH6Dod8A3mvVBqhzziD7e/jKGhbRQ+DpS+DYg/wa6/1ow//BbOqp9yA5Mbc/gOIntuK/uuyOfPY9bwd6EnPmEXmJ5OqjQK+JDUwoKCmIbNmzQ9MoqnqWmpiraTv95Mh4BAcfbt28bT0TiJel3QL8HnqSLgHh1R2VPTPgrBf+nt865Emo41tPxWcpBxr0MoE5jyOuos2eDqg1egQtScDztKcj7tDFLgUOHDikiJ+tgwqJfkd0rd0cpvgutzW2AJkTIasXazgpoaqclPzNGxqm1tzJk9RrAEalISq+CRvJGqI9EbJ0+DK6ug/HFulPItG8AuVxe+NcAtavrqrYWmno0B64dw/GL6i6ccvEg9ij2oSW6N68PY6IfCtGeW7VqpdYO67old5TcvEpcnxJ+ZKZmzalJkyZF0eatuZ2W3DZd0lLPduUh/eS3eMfVAwN/jEW6wm56AiatfwivHjUQM3MkBs87hDRagOuV7PH6u6PxgeN2TBr+MeZv3I2jMbGI/esAIlYHYcQH/0GK+wiM8n6lcINSL6JFmcipDM0yrf2Ulbu7OzevKup14y6s1UxTGQ36HQwePBj0u+BJogiI1sTkXWKhPnKGloFszel77FlCKPMhvfTgMJaUn85OzvNmkE3Q6Btae93PWPLhZWxES1kJ/bbMO4j9ejGD6eOiWpNOmnRw8+fP1161lbxJSEjQqpO3kiaWeTNo/BCO1p7o97By5Uprb6bFtk9d6Wv4p6QwWnizL8dijFdtJG+MRhQc0a1vOzSxkaF6Kzcg6zKSkp8Bcpme9KtB/tYkbDozDLMvJiLpbgZe2NZE/Vdd0MrtVdTTqS7RXYU1uZzU1VLBpIoOYwjXuvLzd6oICIdYrMmpkmoLi+/I2dLWrVuLH/ArSSEgXt1RGC28oFUZSIwlvxGe6Nu2MSohF5kZaQCqo2rlEiddtACRi0fxUYjYdhy3K7+C1p16YYCfH/yG+KK7ZwvUw00c+TkUm2NTjQqftXbtWoVjfC2VW9Vjbl5lfHda8yEWdVSaNWumCL2m/pzfSwMB8UK6gSu6dHPEje3bsG1fBDaHxQNtfND79RrISNyN0DX7AffOaPdqDT1b/Aw39y3E0Hc34Wx6Xoky7OEprBoZiNkHb6Dk2xLZVR4Is6OKMrPkh1pUut+gG2s+xKIOhPB7EH4f6u/5ffkiIF5IV3LH0PlT0PPSIrzv8wnC0tvhw5nD0L7aZYS9PxqLL3XG7O/GoouDrqoofNZk1LGxgY2NPbyCDgH4AUOdqoAc9yv/2TZ5H1vQDB4NHQw2vxNmR+ULuflqp0MYp06dMl+FVlQT4SYILytqltam8FWXVmjK/YWJIrO8REbSGfx97hGqNn8DXTzkqG6TgXM7DyHD9S286VqndF8bL68iYvYi/cNnfegLV5luIzz1yCwVLRqFEMuOR2ox7HcmRGKxltiX+rSeYjjSeJk+fbo+2XkeMyJgIiFtSo7LLnwW2Q6TU6WuXbuakmFJ06IP1dmzZ9G2bVtJ8ykl5uLi4hRHwQsOrUqJs7Lj5fjx4woXt9ydQNlhbCxlo4R0QbTwQ2gaOAdT3kzHlskLsfsJnf/TkkqNFq6lnMjHyjPpijg7Ivgogji5pPTz8xOJZsUpHhERAXL0v3ixzujJVgWIsOpKTU21+jMEltZxxpngKaKFH8LL4S8B5OD+8d8Rdrakv7oiMEqNFl6Us8wuBM931haJpTTAyB0lCRwupEtDqvg94UW4VaQk/C5u3brFhbTEOl7Xbp5WVit5fo4z7BLWDHACKnni8zOZ5MlI+58ZgspqZbbwBXn6skb/0aW1m3wzkK8SnvRHgPBq0aKF/gWsJCf9PiieI0/SQsComTTLuo3zCQ9A82j9kgOaerqgnt620vpRNSRXRZwdET6CbwYecFS/0UI4nT59Gtbu20UTGnzVpQmV8n9mlJDOS9gCP68g6B8dbTzCk7+Dn9yo6kyCkrV7vtMGkuARjy9jtSGk+pxwqgi+XVRbXXDHPeJpQqX8nxklNSs1fRsrwsPxTME/w4uknZgdtB4pHfzxxYd94NmwJvD0Nk7t+BmrtubCL2Qo2jnqNpcrSyiE2VHTpk3LshrJ0iZPbufOneMWHnr0EC33rd3znTYY+KpLGzLl+9woIW1TzxPv+BWGFGK3sfPThbjSZRFO7v0XOjsUC+OhHwzAGzUHIDDqMv75SR8TtfQFUmK34D9TgrH4UAoAObynfo3J7w3AwPZyjQdchNmRsDliIkYshgxZd5C6h6fSESCcCK+KmPiqS5q9btTGoUpTHsVj58ZYtPDrDS8lAa3IU7kp3hrYA1n7IrDv0lOVYsbe5N/diZkDNwFjtiE5j4HlxWJRo2P4eOBKHNJiBliRZ0eEc/PmzRU2sMZiXpHKhYSEKPCqSG1WbiutIvjmoTIi5X8tXkhXs0MteyDtfzfxQN1nNHuMq/GXANRHHXujJu1qCD3D1chfsc5jBMaO6gg5cW8rR8dJ0zDP4zAiY8iZU8lUkWdHhAYtYymRLSxP2hEQ8BHw0p7Tet/wVZf0+la8kLZvA1//N5H+33mY9u02/JV4CykpKbidGIPIdfMxe+kZtPx4FPq1NDa2tzJoWbiTkAR522ZopMy5bT00a/scGyPPQT2WC5WmTUOaTVbUJCxjuWN33SOgogSE0IUCX3XpQqd83imLOuM4sGmAnjNXI2xCTUQEvYsubk3h5OSEJm4d0DfwJ9ztPxdrZ/lArq+nUl1c5D/CjbhkrTlS4m7gntrBR2HTsCLPjggwWsbycFpah47iRUUIl6UbAb7qKg2f8nhvCh0EbGSvY9TKXfCecAanY88jKe05IHNCm7ad0NmrOWqbyj46KxkJ51MAA9xQCJuGNJusyIkvY0vvfTrwVFE3DQV0lFddFXWjXcBCKv9NIqQVjansAGdPb8WfVBpHfJDpWUU1qVLuB1rGDh06tEL5o1Buvz7XtGlIzqgqehJWXRXJEZmU+1y8usOcrZM5wc1DblCNfHZUAJeg7hE2xwwCsQJkFnARcKoATdbaRFpN0O+GJ2kgYFlCWrFB6KQVuRIbioDC9KwibxoKYCkvY4Vn/H8xAnzTsBgLvnlYjIUUrixLSEOGxm7NUWKDULGhmAEPNydoCnXLZ0cFQ01Yxkph4EmNB75pWNwjwu9FWF0Uv+FX5YGAhQnp6nDxfR8B55dh/voLUDhHzU/BqeULMfP8ewge5lrixGFF9cOgaTDxZawmVAqecbVYMTaWvuqi4B5RUVHFDbLwKwsT0oDtK30QvOkLNNroA3uKf1jJCUPiPPDdjonw1hBHkW8aFo9QvowtxkK4IhNNCh1Fm4aVKhW7NBDeV9T/lrzq+ve//41Vq1YpAl5Q/1p6sjghDTjAtVcAFh1MLvJfnbxhCvy0+O2o6CZVygOUL2OV0QAoWk+nTp0wevRoxQuagf3999+qmSronSWvuihU3C+//KII3FC3bl1QpB1LThYopA2Dm28aFuNl6cvY4paY5uro0aO4evWqCrFvv/1W5b6i3lj6qqtGjRrw9/dHQkIC9uzZg3HjxlmsWwSjYhyaeuBSLEKeOAIcAY5AWSJgqQGZJTGT1hl6S1dYrlLeUYeXFW1LpRseHq4II2ap/JuSbwq6qp42bNjAx0zh74o23Y8dO2axeJBQHjx4sGK8U4xTUoNYYpKEkLZE4CyVZ0tfxpoSd1L/0HKY0ttvv63QY9ISmacCBCx185D2GhYsWICPPvoIn3zyieKUrSUfcTfdsXA+si0CAeXNQ0seuKYC287OTkHq119/5VGy1UClzUNLDBbRo0cP0Cbw3r17raJP+UxabWBa+y3fPFTtYX7SUBUP5TtLXXWRNcf06dOtQkBTf3AhrTwqK8i1pS5jy6J7+ElD7agqr7q055LeG2tbIXIhLb0xVuYcWbINrKnBKXnSMB9PoqfDiQ5KafhzGr0EEbEpUHNbbmq2JEGPr7ok0Q18Ji2NbjAvF5a6jC0LlLTHNGyPqQceqlk2PEZ0j0v4zGsclsZmlAU7kqPJV13l3yV8Jl3+fWB2Dix1GWtqoAQHQgIepdN3gPuYIMzzOYOg6RFIrADTab7qKn1UlHUO8UKaPUT87m3YdvQ6npXgluHZ9SP4+YetiE3PK/GWPygfBGgZS/ajFT3moahNw/NXcSfL+qU0X3WVz29UuVbxQjrvFvZ9/i7eXXsW6cqUFde5eHhqPUZOWIWDSTkl3vIH5YdAx44dK3zMQ9o0JFMtY5J8VB94aXDoZQwtKZcRVhnCqkPKvForb8YJaXYXOz/2KNhYqeKFoGsAwoZq2Gypiibv/xeQNUZDxyrWiqFFtsvd3b3CR9+gTUPCQe8kuMWNegP/fO8NOOhd0HIz8s3D8u87I313MLxM2o7Zc/9Acm4qLm7bhdiG3hjetQlqqLepxivwGuiPD99xh8zMLjpod56OEfNUEoHExES4ublVaHxofNCJQ1dXVyWAyLpjJtx7L0SK0tOCSzm8p36Nye8NwEAtXhdLFLGCB3R6j8zayvQ05pNoBLuPRNy8aOwJcAcS16Gf2yq0PbAXi3rV0wPFJ0jctx7rk30wb7S7VVlEGHni0AZVmg/Bwv8OAfLisaLDYSR0/Be+XzMA9fWAk2cpfwScnZ0VTNAy1trsSvVBV1i+CziULEPWHfoKiJKlrekJrTbMffLQ1jUAkSxAfxifxCB09DeIm+ejfxkLyWmkkFZqXSVPfH7mCT7Juoek+FjcylV6V3TpgKaeLqhX2cxT6aL6+YU6AuTKUdg8rIhCmjYNqf2EA0+6EWjTpg2PNK8bojJ9a5xOWoWlPGRdDMO4N1zh1tYLXl6a/r7FkYfcukMFNgnc0OYheQqriIk2Dan9PJWOgLDaEFYfpZcoLccLpMRGYMnown0tp9FYsucM7ikVy09cB18bLwRHPyp4mpWI6HXB6Fl0wMgXweuikUgWNgpVSW8sTklB1NhWqOQ0HdFPyPJGrR4q2zMY66ITC0LvQTi49B5+ij6EDcG+hQeYPDB6SWQBbWWeUk7pzpOfgtgNSjyq1KVEyMBL8UL6xXms++gLrE95Hf5zf8Sv4eEgd5gqf3+MRDtHHprIwL4p8+y0jI2Pjy/zeqRYATn8N2jTUIqNMBNPyqsu8VXmIyv2e/zD6wc8HLwVmeQWNXEamp/Zh7CSmwCF1WUgds0/MfJwa6zOzFPso+QlT0GljR9h4m+JyHfohUWXD2CqXA6f0EvIS16AXg4oqGfgdlT6NAp5Cverz5E8yw4be/8Ta1QOI23FR3OjYD92ayHtpXhl16cYvyamUJgD+XcjMK79EKzHeCQQD5m/oMf5KfCetA136XuQfxMR43wwMLoJFiU/B2N5yFzdGodHDsWkiJviTqgysSk5nPkDTD55L0vNF0vMtOUL3EmblqY1UUtISKBdVWtqkt5toXZT+0umPPb4wDQmR3s29cDDkq8r6JP58+ezlStXmqD1D9mBqe2ZfOoB9liZ2uMDbKpcznxCL7E8xlheQijzEfog7xIL9WlR9E65WNG1WnnGtNSjQktbXxeUhU8oSyBmWA5LCB3OIJ/GDjxWPCAOC8fJcBaa8FTpOqeIpaI8KuWUXut5KX4mXbM2GsmByvZ2qMZVzuInGmakICxjydKjIiWhvUL7VdtuC4deC5DMYvS0KlAtba13Jlt1PTmHyI3J8HBzgkwZLJkT3DwK3MYqP1Zc2zaC59vuiJr5X2w7FY2IInVFiZxKD+qh16IYJC/ywr3o7Yo4hxERPyG4dy+MjcpWyqfpUobGbs0B4cBS/g0c23IM8HBBY5kgMoVx8hsCXLMRExmFFLkLmjWqqkTQFrLGLvBIiUJkjPEBcYUalQgbeOnQEf6zRyB963bsu/UU3ODNQPzKMTstYwMDA3Hjxo1y5ML8VVN7qd1801B/7GnzcO3atfoX0JIz/94NxGlVa2gphNpoP2UzEjZ1Qkb4Igzt7QZ7Gyf0DF6H6MQnWgrlI+vyBox2qgW33qvwdwbpJBrAd3UEQn2A8wnJRaoMLQQMf5yyEL1rVVJxzFXJbSyiDKekUkK8dUdeMi7EPkDDy1vwbtPNaN+/J16rq0bWth0Cl05Ed66XVgFfCjeenp6gmaWPj/WZLmnDl9pL7eZJfwQEW3LCTrjWv3RxTttGzdBWDsQVP9LzygGuvfwUfwGLaENwJ35e8RV6e1/Fgcvz0EudSn4ifps0Dfv6hePOT354RZiO0ibj+RSgLCJp+YQiYU8AXIW61Hky8t4E5HJwP/Y06NAhkILYXZsRFham+vd7Eh5rNM3TxHUuHsVHIWLbMVx/pmFe/uw6jvwcis2xqXzWrgk+A5/RD27//v0GlrLs7LRZKkbQWHbrjefeJKsuh9fhO8qp5Ew2KxkJ50tTQwi8V4W8/RB8NHog5ClXcePeC+FF8X8FPcCja2vIlaRcfmYGCu1FivOWdmXbDN1GdCtWfxTmL7BAcYLvugdo5+sD+fkzuJCizAttki5DT5v3sC6xpGej0qoV3iuxLzwy8L/CTjpTsSuqNUho5goMqK+vdccz3Ny3EEPf3YSzGpwysYensGpkIGYfvAFu1GdgX2nI3qxZM2zfvh0UF64iJGonLdup3TwZhgCtPmJiYgwrVCJ3PXh/Ph39Nk7CxHUXClQOWZcRMX8RFmtTg+RfxjpfF/QMjig2i8tKxP7IWCDgffi6VAeUddrZWciSFXwMojZuwaFCwZmfchzLp3+FddrqKcGr8KA6XPqNwzS33zD3mwNIUVhz3MWh9VsQ5R2EBe+5w9F7PL7rdxifTf8JpxT15SMrcRvmTvkeCJmC91yrC8QM/i9eSBdWyZ7dReyu9VgS/DFGf/gfHE1/iiu7whAR/wClT6Jz8WDnZNRR2EDawyvoEIAfMNSpiop+h47x2jZ5H1vQDB4NHazq6KfBPWeiAsKMkqIpV4QktFNod0Vos6naSJidOnVKNDnbV4Zg+aEl8Dj8AezpN28/CX93CECIj7aNQ3eMWb8FE+tvh7d9oc7Xfji21x+PHfMGFKgybJujX/AovCA76ZoB+O2qDN6TV2F9xxPo7VRNIUcaf3kSzqNXIXxqe4PbYCt/G/M2b8aYvCVwqmQDm0odMDdvJGI2f4r2tJlo2xR+y8OxqcctBCvqqwR77+2oP3ELNv+zo+omqYG1G+m7Q7UWln4S344JQNCflwtfjEd48izUXNQffUOdMHvbj5jVuzHUNNWqRF5eRcTsRdienI3UiwexK1YG7+Gd0KSG+nfEDnKvgQj40BeuMt2zc+67QxVibXdTp04F+Q328/PTlsVqnlP8OzrivHjxYqtpk7kaQodZyCImOzubb7qaC3RAt9zUiw/2AAcXTUFQ9GsIORKOjn99ih5TqWRD9A7+BsEn/oE5kzei399forOdFhs9lorEMxlw+WQZ1jvb4NyKYdiV0BL/+n6ZAWoSvbjlmTQgQDv3JLgqgpCmdlJ7eTIcAcF9ADmlatu2LHbeDOepIpRQn6Ya3ubMC4gMOwHHkWPg360JairJ4cpybwRM6ANc+BtxN3ToPB+dxNI+HeC3JQF5qIQaDT3hP6w5aumcehvOKi+hGYEWLVrg0CFSMVl/onZSe3kyDoGgoCAkJSUZV5iXMgoB8UL6aQbupQB1WshRR0lAF3BTGfa16wB4jKwc0rZrSbkvkJMFZF+7iqspd3H94lGErY/FlVspSEnR9PcAGc900NNSDX+sGYFWrVrh9OnTSEsz3uBeM2VpPaX2UTupvTwZh4Cw6jKuNC9lDALihXQtOVzbyHD/zFUkq1vMsUc4d/QUIHNHcycdu5sN38DggHZIWfM+Wjm5oO/cEwA2YWxbZzg5OWn4exOTdt81pr28jAYEBMfuly5d0vDWeh5R+zp06ABqL0/GIfD666+DgvfyZD4ExCsU7Dww5NP++ObjRfiqhwMGPCY7wadIvxmHyK2rMPE/V9Dy46/RpZGOqmyb4d3lm7Gz4x5cyszGnUP/xfJdDeA/awg8NIYoqgrnFvbmQ6kC1ERhpMgzXNeuXa22tWLCZVktKAY2TDmclqCjNpAEz24oAnr6+NCd7eVttn92PyaD4nyJwmkPObABZKzliOXsxIOXusurvM1iccv7Msgmsh0PclXeGHpTUZ0HGYoT5Q8PD2eBgYHGFLWYMtQ+aidP4hAYPHgwi4yMFEeEl9YbAZOY4Ck+DCwbKedP4WTMeSSlPQdkcri91gHdu7REbWOc/RO9M4ew5+ARnDr/GC6Bc/BFo9P48bwThg3yRH09aHITPP0/2XTcl8JpWat5FR1isbOz0xAuS3+MeM4CBCicloODAz777DMOiRkQMJ2QRj6eZTxCeo6Gc4A2NeDYsDaql9hY1NJC9gh/ffsJRgZtLTxu3gL+4fuxrOZ3cOn7G9rODsXPs/pAXoqg5kJaC75aHhNeJWP+aclsYY+FjxCPeSm+46KiorBq1Sps27ZNPDFOoVQExG8cIg9Zidsx//3OqO/YUMMmnxOc5F9i973Szx0WcJuHtIPL8WHQabwWcgg3Dy9EgcFUJdTpPQm/BLfAwTkLsC7mcamN4xkMQ4B8M1AEbWtM1C5qH0/iEahorgTEIyaOgo7dPD0J5yfhj+DJmLmtCrxHTET39k3gUGLG3Awt7PX9HqQjLnIPLjsORoh/VzjdPl3MSGVnvB0wCj6LpmBv3B182bk2dJ85LC7Kr0pHoHv37lZ7qIUOsVD7eBKPgHCknh9qEY+lPhTEC+n757F/2w3IJ+9F+FJfDbbS+rChnCcHGfcygDqNIa9TGVBzKWFrXxuNkI7jWc+5Fzxl2ExwTeZVo0ePtsoj02Q2VlHjOZpgaJQgQYdazp07x08elkDG9A/0nd5qr9nkkVns4eTqDNy/hKvJym7/iIU8pJ37C/vQEt2b1+ezaO29YtQbZfMqowhItJAQQFVon0TZtCi2yNcLxYnkqewREC+kHTpj/LKPUf3XLYi4mKaHx7vSGlULbYd8gEH4DbO+Wo+TN9KQhzzkpN9AfOT3+GLiaqS0HIChXeQooVUpjTR/rxMBOuQxePBg/O9//9OZz9JeUnuoXfwQi+l6TojUUlFc3JoOOcMpiRfSsMOr/Ubjo2Z/wr9NXVQpCrluU+xm1P5z7HyowepDI782qP7aaKzZFozGv4/HW8MW4gZuYGvgW2jbdxLCMBhLNgSjv7yKxtL8oTgE+vTpYwKfweJ4MHVp8oFM7eLJdAgI8SEF16+mo8wpqSMgXifNbmPXl58iaN9tQNYe/Ye8hrrqot/WUGdJ1SDvPR27Ewfh5MkYnE9KwwvI0NCtDTp17wTX2lxAq3ekqe7btWuHL774AtOnTzcVyXKnQ6Ziy5YtK3c+rIkBIT4mWc0IG4nW1D4ptUW8nfTDnZjQfCB+G/YzTq9+Hy2qq0vo8msut5M2HHtyQlS3bl3QDMkajv0KPpCtpT2G92jZlaAweSSkuW/ussOYKIufSVezQy17oJZLczQ2VkDnJWLL5IXY/URfz3Z28Aicgynd65ctOhWQsFmxzgAAFUBJREFUuuBsifS41iCkqR3kVMka2iK14WjN1kBSwlq8kHboiLGLxuOPlTuwf5QH3mlS04gNvRzcP/47ws5m6YmNO8YPf6lnXp7NUATI2RLpca0hgji1g9rDk+kRIDcClMRGEDc9Z9ZFUbyQzkvG2b9T4HDpBwx4LVKLTrodApdORHdHLUdPCoPZfm5d2Fpsa7y8vDBz5kyr0EuTPnrevHkW2xdSZlzQS9NBIa6XLrueEi+kkYP7J6IRq5gEx2LXptiS3MpqYTgPKVcSF4k+ISFNzvFJn2vJagLin9rRunVriSJt+WzRKU6yl/b397f8xki0BeJ3+QpnweS4Rutf5goeq1CiA0ATW9ZiLy3YR1vyh0ZT/0jpGeml165dC24vXXa9Il5Ilx1vnHI5IkB2xfv37y9HDsRXze2jxWNYGgVBL01+PHgqGwTEm+AV8sWe3cWZA/tw8MjfOP/ADYFLx6HRiXCcb9wXgzwbmMCMxHAAuAme4ZgJJY4fP45u3bopVkfCM0v7T/1/7Ngxq442I4U+GTdunMJ5FVd5lE1vmGQmzdJP4tsRfeA14EMELV6DsPWX8fBZBpL2LcXQbmMw98AdExwXLxsAOFXNCAjBWuPi4jRnkPhTsjigJLRD4uxaNHv9+vVDRESERbdBysyLF9LsAQ4umoKg6NcQcuQiDi/2LmxvQ/QO/gbBrf7CnMkbEZOtHqW2FFgoMkvsbqxb8iUmjP4YS44+RN6V3VgdEYeHuQbSKqUq/rokAqSXJv/L5OnMEhNZHBD/3F9H2fce+fHYvn271UebL3skNdcgXkhnXkBk2Ak4jhwD/25NUFPJ61FluTcCJvQBLvyNuBs5mjnQ9FQRmWUMunv1x9igRfghbB/OP3yKx0nRmDF0EEbM3Y8ULqg1IWfSZ8LOvUmJmokYWRxw/9HmAZvM7+jAEO0B8GR6BMQL6acZuJcC1Gkh1+BLujLsa9cB8BhZOfqeJuSRWUzfzcZRFHbu6ai4JSXilywOiH+ezIOAcADKPLVVrFrEC+lacri2keH+matIVtdCsEc4d/QUIHNHc6fqeiJbHJllHEVmqalkyi1EZkG8IjKLvn719KyYZ1NDoG3btoonly5dUnsj7VuBX4F/aXNrHdz16NEDM2bMsI7GSKwV4oW0nQeGfNof+GURvvrxKG48Jkf9T5F+Mw6RK6dj4n+uoOWod9ClkZKw1QmCWmQWtbxCZJYUHplFDZmyuZ0/fz4OHz5cNsTLiCrxS3zzZD4EhA1aS91oNh9ShtckXkhDhtcCl2Db7Eb4fcI7GDbvBIBNCOzSAX0nbQVGzMeGr/tBrqSr1s0mj8yiGx/zvrXEGRLN6IhvnsyHgLDRTCaPPJkWAX2nt7prrdwYvf+9Ecc8diL28ROkpT8H2H0kpnhh8pxhaC3T4rNDI9XCyCzf/AuzvuoEpwHKkVn+wFJFZJZxPDKLRuxM/1B5hmQJ6gNhJifwbXpEOEVtCJApHrkv/eyzz7Rl4c+NQYCZIOVnxrOwCd2YTD6NHXicp6CYe3E16wYwWc+5bH/yMwNrecaS989lPWWKWLOk6S7+a/l/bMmJeyxfD4pUjifxCAQGBrKVK1eKJ2QGCsQn8cuT+RG4ffu24ndK/3kyHQLipVj+fXYg+E0GeLIR83ezazkF4jM/8xo7siFYIWhlg0NZwgt9xKpyw/JYTnI8iw4PZctDQlhIyGoW9udRlpD+QjmTzmsupHXCo/fLyMhI1qFDB73zl2dG4pP45al8EBg8eDDbsGFD+VRupbWKPxb+JBrB7r3xU99wXAj1g5OK7jkL8SveR9tJdghNCEOAq74WHgBys5CSlITkTE1+oyvBvmkruNarpnPxwI+F64RH75dCtJazZ89CyioPUnVQ+C8ehUXvrjV5RlJ30OlDchHLk2kQEK+TFuykWzdFAxUBTQxWR4PGjQEkIC0zV2+OWdY5/HfiGIxdf1ZLmRbwDz+IDX7OWt7zx6ZEQPCKR5tCUhbSxB9FBede70zZ+4bR6tWrF0aPHm3xbm4Na3XZ5hYvpOs0gYenDGFRMUic9AZaV1GS1EV20p0MsJPOxqVNszF2/T108J+D8e+0hqMyTQUeVVC/HR2S4clcCPj5+eG7776T9KYQ37Qy12jQXg99IOlDGR0dzX1Ma4fJoDfi1R3IRuK6cWg/9iBajZmMf47sjpa1q4Jl30XsznUIWXwAVYK34fjC3hpOJGri9TYiRvfE0H1+2HthIXzrGGIZokqPqztU8RBzJ3WVh6DqSE1N5f46xHS0CcpylYcJQFQiIX4mDTu4+i/GrrRgBAYF44P1StThDO/Ja/H9TG89BTSVrYHajWoDle1gV80EZtzK7PBroxFQtoOVosqDVB3coZLR3WvSglzlYVI4YYKZtMBQPp6lJCL+0jXczXgO25oN8GpzN7i51Ed1JQ2IkFv7f4ZnCRswpsuPkK/biIWDWxhYvpgyn0kXY2GKq6ioKEXsQzrRR/HtpJIoKggdXqFYhtYQPFcquIrhg3x5UOAIbjMtBsWCsiYS0gy5WXeRmHAf6r7uWPZ9JMSlo8XI99FZWyDavERsmbwQu58ITpie4tbxSBy6lgVZ+/4Y8lpdqM6p7eAROAdTutfXiQAX0jrhMfiloPKgWWvXrl0NLl9WBYQABVzVUVYIG06XLDy++eYbnDp1yvDCvIQKAiYQ0nlI/2slxoychT+vKaLRqlSguJFNxI6kZdrjHObFY0WHbph0Vkv5EhTdMX7HAawZ4FTijfIDLqSV0TDN9YIFC5CRkYHFi6UTWXjq1KmoXbu2VUQ3N00vlT8VqX7Qyx8ZwzkQL6TzL2Ndv14Ye+JV+E/uhRrHNuCHGBeMn9oFOLgVPxx8BcF7wzDP19nsIbS4kDZ8QJRWQmqzVi4MSuux8ntPH09KUvqglx8axtesqkUwhk7qVZw6kQLHkdMQMmcmggPeArLqoeOIWVj95y9YMeg2IrbH4aG6G1OtdeXiUXwUIrYdw/VnGgo9u44jP4dic2yq4qy4VjL8RZkgQGoOcvC+c+fOMqFvKFHig/iRkvrF0DZYa34yxQsJCeERW0R2sHghnfsCOVmC0/+qaNDMBc5IQsKdLNjI2mDAsM64snoL9t94rierz3Bz30IMfXcTzqaX9BjNHp7CqpGBmH3wBkq+1bMKnk0UAl9++aXCZpo27MozUf1ku0388CQ9BOjDSYJaKh906SGkH0fihbRDfTR1BtKupSCN2aBGwyZohQdIuJsBBltUrloVwF3cT9N0vFtgMhcPdk5GHRsb2NjYwyvoEIAfMNSpCkhlofxn2+R9bEEzeDR0UNtMFGjx/2WNgLe3N06fPo0zZ86UdVU66VP9xAfxw5M0EaAI4vQhLe8PujTR0Y8r8XbSNVvj7THdMHfZQgS3dsTigFZ4q006vtnyG3a6tMP1P44Bsu5wrk/CWluqjAa+n2Htl0+xPTkbqRcPYlesDN7DO6FJDfXviB3kXgMR8G5zLqS1wVnGz8lmeuXKlYqlbHmqGWgpTXwQPzxJEwFyXzp06FBQzEluHmlkH5nCcVT+g6NsyQhPBp9QlpCn7mbUmfWcf5Sl6e0EL4vFLe/LIJvIdjzIFcUe94InCj6dhQW3lMeOHdOZr6xeUr3Uv9wtZlkhbDq65D6WvOPxZBwC4q07hI9D7hPcSclFI+c6qIyXyEg6g7/P3QPkbdG1Y1PIDDrQIhAV959bd4jDr7TStHufnp6On376qbSsJn/PLQdMDmmZEeQWOOKgNZ2QFsdHmZTmQrpMYC0impiYCDc3N5jbhangpyMhIQGurq5F/PAL6SJAeun9+/dzF6ZGdJFRQjovcQsmz9+NJ/pWaNsOgUsnoru2E4f60jEwHxfSBgJmRHaa0ZKwNqf/YDpyTMKZ298a0WHlVESYTUdGRnLdtIF9YJyQjl+BDm0nQZu35xI8lHbisEQB0zzgQto0OOqiIvz4zHVUXGqHaXRhw9+pIkDe8WhGLTXfL6pcSu9O3XRCLw4reX6OM4xR6C39/jJXaD8SrleNPJNUESDLig0bNuCLL74oczMrMuOieqg+btEh1RGhna/hw4crXm7dulV7Jv6mBAJGzaRLUCmLB+wJrh+LxN79x3HqRjrybR3RtG07dPLuB1/PBnodMecz6bLomJI0SXiSFzryeEZ2sWWV+EysrJA1H13ypOjr68tDnBkAuYmENENuxhWciIzGsTPxSLiXDVvH5ujYpSd6+3aBa+0qBrBEhlX3cOTrAPT/eg9KulxqhzFhm7B6VGuUFjGRC2nDYBeTu6w388prk1IMJrysZgTK0ypIM0cSf2qc5Z5yqXz2MjmKze7prLBbJRGr/CfrOZftT36mXKCU61yWemAmc4cjaz8hlJ1MSmWKAOQvM1nyhZ1s3qAWDLJ/sNCEp6XQYQo+Ss3EM5gMgfnz5yuiimdnZ5uMJhEiehQFnOjzZPkIpKamKvqTRxXXry9Jpywu5d9k4R+6M8j6suBf/2Y3M18yxvLZy8xkdnH/CubfUsZkg0NZwgt9T7M8ZAemtmdwnMR23CdayimfPY9bwd6EnPmEXmJ5yq80XNPHgifzIUDClA4tBAUFmbRSokd0TS38TcokJ2YQAmfPnlVMosrrMJRBzJZzZqM2DlUWB4/OIWrrZcgDJ2Pqex3RREYnzW1QWSZH694BCP6nD7K2/4noK/o648lBxr0MoE5jyOuon1q3QdUGr8AFKbiW9hRCiAAVfvhNuSFA0Vpo9/7QoUOK/6ZgRJmelKLBmKJtFZkGhWCjDeBu3bopIotXZCxKa7t4IV2pCqpXASrb26FaiVOFVWHvWAvAc7x4SR9OfVItNPVoDlw7huMX1S2xc/Eg9ij2oSW6N68P40PU6sMHz2MMAhQtmqJyCJt8xtAQypCAFoKaEl2erAsB2mQm3ysUif7OnTvW1ThTtkb0TD7/ITsxvz+TtRzHQi9ksGKlRj57mfYXWz6oGZMN+oFdUCiW9aktn724uol94AiGlv9g88J2sSOnY1jMyf0sfNVk5i0Dg/tMdiC1dL8eXN2hD95lk4d8agh6ZEPVFJRf0G9z3xxl0z9Sokq+PWiscNWH5l4Rb92RfwvRyxZi7r/X4FBWS/QcPwL9XGoBTxKxZ/MvOHjNEd7jA9DfRVb4bakK57f9McKzto5vzXOkHFmNLwJnYcsVVfsOmXcQ1n4/A++1roUSE3c1ity6Qw0QM9/S7EgIREqnA/U5wk1WHIJfDppJ8xm0mTutnKoTTPPmz5+PCRMmcDt4pX4QL6RzY7HE3QtB15So6rxsAf/wg9jg56wzFxmJKILbXkxE0t0MvLCtifqvuqCV26uoV10/LQ0X0qVAbIbXZENNhxdGjx6NoKAghRP4Vq1aqfwI6dTipUuXsH37doX7U9JV0sEHroM2QwdJqAr6qH/99deIj49X2NuTa1N9PuwSakKZsCJeSCMXWY8eIVNvnXMl1HCsh9paBS2Fz4rGket2aNe3K16trjZfpvBZ4dG44z4EH7Svq3M2zYV0mYwZo4iSIKYIHaSvJmGsnigEFs26BwwYoCLA1fPxe+tHgI7+09HxGTNmFDW2IjvTMoGQJhzz8Szlf4hNb4Q3W9dFXsoRrJo+HTN+f4n+X87AnEkD4CrTd5svC7FLBsIryA3hyd/BT65q4cFub8EHTd5HTEgMLk9pr/PkIRfSRWNcUhcksB89elTEU7169bhgLkKDXygjQOovSs7OzhV2ZWUCIZ2H9JNLMdRnKuLG7sXVZa1waKwvhv43D9795bi96wyqBG/D8YW9UUdtUlzcGRQ+awrcBy5HevFDHVfNMCQsCuGjWuqMzsKFtA4I+SuOAEfAIhBQnaYaw3L+Ffzx72U4KA/EmpFtUfPKLvzw38vA4DCs+2Mg7i94F12++R2HJvUoMSsuro6HzyrGgl9xBDgCHIFiBMQL6dSrOHUiBc2+HIsxXrWRvDEaUXBEt77t0MRGhuqt3ICsy0hKfgbIBQuPYgaKrqq4wG/hT/DDU8SvGIZdCS3xr++Xce95RQDxC44AR6AiIiBeSOe+QE6RlVwGEmMvAPBE37aNUQm5yMxIA1AdVStr1XWo4V4Tnp/vAftc7TG/5QhwBDgCFRAB/WzZdAHTwBVdujnixvZt2LYvApvD4oE2Puj9eg1kJO5G6Jr9gHtntHu1hi4q/B1HgCPAEeAIaEDABBuHuXh4ZDFG9J+Bg4oZdTt8+OsW/DAsG6s7dMOkK90xe9uPmNW7sU5LDA28iX7ENw5FQ8gJcAQ4AuWMgAmENLVAiA7+CFWbv4EuHnJUt8nAuZ2HkOH6Ft50pQji5k9cSJsfc14jR4AjYFoETCSkTcuUqahxIW0qJDkdjgBHoLwQMGqCWxAt/BCaBs7BlDfTsWXyQux+osNxaDlFCy8vUHm9HAGOAEfAVAgYJaSRcx/Hww7h5fCXAHJw//jvCDtbZOJRkjdZLQxfXPIxf8IR4AhwBDgCuhHg6g7d+PC3HAGOAEegXBEwaibNsm7jfMID0Dxav+SApp4uqKe3rbR+VHkujgBHgCNg7QgYJaTzErbAzysIensnxXiNzpKsHVzePo4AR4AjIBYBo4R0paZvY0V4OJ4pamd4kbQTs4PWI6WDP774sA88G9YEnt7GqR0/Y9XWXPiFDEU7R3294IltEi/PEeAIcASsBwHxOml2Gzs/fRcD497Dyb3/QmcHJWGcew1bxg1A4N1PcGzbZ/C00/douGkA5iZ4psGRU+EIcATKDwHxx8IfxWPnxli08OsNL2UBTW2q3BRvDeyBrH0R2Hfpafm1ktfMEeAIcAQsFAHxQrqaHWrZA2n/u4kH6gHB2WNcjb8EoD7q2BulWbFQWDnbHAGOAEfANAiIl5z2beDr/yYWL5qHaa1t8fGgN9DUvgpyM+/if0c345ulZ9Dy483o17K6aTjmVDgCHAGOQAVCQLxOGgDLOodNQZ/ikzXHoHqkRYaWI+Zi7bKP8Za8mtlh5Tpps0POK+QIcARMjIBJhLSCp9wnuH3xDE7HnkdS2nNA5oQ2bTuhs1dz1C4n+2gupE08Wjg5jgBHwOwImE5Im5310ivkQrp0jHgOjgBHQNoIiN84lHD7GFPfyZQws5w1jgBHgCOgAQGrFtIa2ssfcQQ4AhwBi0KAC2mL6i7OLEeAI1DREOBCuqL1OG8vR4AjYFEIcCFtUd3FmeUIcAQqGgJcSFe0Huft5QhwBCwKAS6kLaq7OLMcAY5ARUOAC+mK1uO8vRwBjoBFIfD/nwsIJJyWWGQAAAAASUVORK5CYII="></p>
<p style="text-align: left;">A point on the graph has been labelled that represents a point P on the spring.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the conditions required for an object to perform simple harmonic motion (SHM).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the mass of the wooden block.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In carrying out the experiment the student displaced the block horizontally by 4.8 cm from the equilibrium position. Determine the total energy in the oscillation of the wooden block.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A second identical spring is placed in parallel and the experiment in (b) is repeated. Suggest how this change affects the fractional uncertainty in the mass of the block.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the direction of motion of P on the spring.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain whether P is at the centre of a compression or the centre of a rarefaction.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>acceleration/restoring force is proportional to displacement<br>and in the opposite direction/directed towards equilibrium</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{T_1^2}}{{T_2^2}} = \frac{{{m_1}}}{{{m_2}}}">
  <mfrac>
    <mrow>
      <msubsup>
        <mi>T</mi>
        <mn>1</mn>
        <mn>2</mn>
      </msubsup>
    </mrow>
    <mrow>
      <msubsup>
        <mi>T</mi>
        <mn>2</mn>
        <mn>2</mn>
      </msubsup>
    </mrow>
  </mfrac>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mrow>
        <msub>
          <mi>m</mi>
          <mn>1</mn>
        </msub>
      </mrow>
    </mrow>
    <mrow>
      <mrow>
        <msub>
          <mi>m</mi>
          <mn>2</mn>
        </msub>
      </mrow>
    </mrow>
  </mfrac>
</math></span></p>
<p>mass = 0.38 / 0.39 «kg»</p>
<p>&nbsp;</p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>«use of <em>T&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 2\pi \sqrt {\frac{m}{k}} ">
  <mo>=</mo>
  <mn>2</mn>
  <mi>π</mi>
  <msqrt>
    <mfrac>
      <mi>m</mi>
      <mi>k</mi>
    </mfrac>
  </msqrt>
</math></span></em>» <em>k</em>&nbsp;= 28&nbsp;«Nm<sup>–1</sup>»</p>
<p>«use of&nbsp;<em>T&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="&nbsp;= 2\pi \sqrt {\frac{m}{k}} ">
  <mo>=</mo>
  <mn>2</mn>
  <mi>π</mi>
  <msqrt>
    <mfrac>
      <mi>m</mi>
      <mi>k</mi>
    </mfrac>
  </msqrt>
</math></span></em>» <em>m</em>&nbsp;=&nbsp;0.38 / 0.39 «kg»</p>
<p>&nbsp;</p>
<p><em>Allow ECF from MP1.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>ω&nbsp;</em>=&nbsp;«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2\pi }}{{0.74}}">
  <mfrac>
    <mrow>
      <mn>2</mn>
      <mi>π</mi>
    </mrow>
    <mrow>
      <mn>0.74</mn>
    </mrow>
  </mfrac>
</math></span>»&nbsp;<em>= </em>8.5&nbsp;«rads<sup>–1</sup>»</p>
<p>total energy&nbsp;=&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2} \times 0.39 \times {8.5^2} \times {(4.8 \times {10^{ - 2}})^2}">
  <mfrac>
    <mn>1</mn>
    <mn>2</mn>
  </mfrac>
  <mo>×</mo>
  <mn>0.39</mn>
  <mo>×</mo>
  <mrow>
    <msup>
      <mn>8.5</mn>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>×</mo>
  <mrow>
    <mo stretchy="false">(</mo>
    <mn>4.8</mn>
    <mo>×</mo>
    <mrow>
      <msup>
        <mn>10</mn>
        <mrow>
          <mo>−</mo>
          <mn>2</mn>
        </mrow>
      </msup>
    </mrow>
    <msup>
      <mo stretchy="false">)</mo>
      <mn>2</mn>
    </msup>
  </mrow>
</math></span></p>
<p>= 0.032 «J»</p>
<p>&nbsp;</p>
<p><em>Allow ECF from (b) and incorrect ω.</em></p>
<p><em>Allow answer using k from part (b).</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>spring constant/k/stiffness would increase<br><em>T</em> would be smaller<br>fractional uncertainty in <em>T</em> would be greater, so fractional uncertainty of mass of block would be greater</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>left</p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>coils to the right of P move right and the coils to the left move left</p>
<p>hence P at centre of rarefaction</p>
<p> </p>
<p><em>Do not allow a bald statement of rarefaction or answers that don’t include reference to the movement of coils.</em></p>
<p><em>Allow ECF from MP1 if the movement of the coils imply a compression.</em></p>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Two loudspeakers, A and B, are driven in phase and with the same amplitude at a frequency of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>850</mn><mo> </mo><mi>Hz</mi></math>. Point P is located <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>22</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">m</mi></math> from A and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn><mo>.</mo><mn>3</mn><mo> </mo><mi mathvariant="normal">m</mi></math> from B. The speed of sound is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>340</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>In another experiment, loudspeaker A is stationary and emits sound with a frequency of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>850</mn><mo> </mo><mi>Hz</mi></math>. The microphone is moving directly away from the loudspeaker with a constant speed <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math>. The frequency of sound recorded by the microphone is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>845</mn><mo> </mo><mi>Hz</mi></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce that a minimum intensity of sound is heard at P.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A microphone moves along the line from P to Q. PQ is normal to the line midway between the loudspeakers.</p>
<p><img style="display: block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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" width="370" height="161"></p>
<p>The intensity of sound is detected by the microphone. Predict the variation of detected intensity as the microphone moves from P to Q.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>When both loudspeakers are operating, the intensity of sound recorded at Q is <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mn>0</mn></msub></math>. Loudspeaker B is now disconnected. Loudspeaker A continues to emit sound with unchanged amplitude and frequency. The intensity of sound recorded at Q changes to <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mi mathvariant="normal">A</mi></msub></math>.</p>
<p>Estimate <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>I</mi><mi mathvariant="normal">A</mi></msub><msub><mi>I</mi><mn>0</mn></msub></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the frequency recorded by the microphone is lower than the frequency emitted by the loudspeaker.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d(ii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>wavelength<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>340</mn><mn>850</mn></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>40</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">m</mi><mo>»</mo></math> ✓<br><br></p>
<p><span class="fontstyle0">path difference </span><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>.</mo><mn>8</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">m</mi><mo>»</mo></math> <span class="fontstyle3">✓<br><br></span></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>8</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">m</mi><mo>»</mo><mo>=</mo><mn>4</mn><mo>.</mo><mn>5</mn><mi>λ</mi></math>  <em><strong>OR  <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>1</mn><mo>.</mo><mn>8</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>20</mn></mrow></mfrac><mo>=</mo><mn>9</mn><mo> </mo></math> </strong></em><span class="fontstyle2">«</span><span class="fontstyle0">half-wavelengths</span><span class="fontstyle2">» ✓<br><br></span></p>
<p><span class="fontstyle0">waves meet in antiphase </span><span class="fontstyle2">«</span><span class="fontstyle0">at P</span><span class="fontstyle2">»<br></span><span class="fontstyle3"><em><strong>OR</strong></em><br></span><span class="fontstyle0">destructive interference/superposition </span><span class="fontstyle2">«</span><span class="fontstyle0">at P</span><span class="fontstyle2">» </span><span class="fontstyle4">✓</span></p>
<p> </p>
<p><em><span class="fontstyle0">Allow approach where path length is calculated in terms of number of wavelengths; along path A (<math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="italic">56</mn><mo mathvariant="italic">.</mo><mn mathvariant="italic">25</mn></math>) and<br>path B (<math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="italic">60</mn><mo mathvariant="italic">.</mo><mn mathvariant="italic">75</mn></math>) for MP2, hence path difference <math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="italic">4</mn><mo mathvariant="italic">.</mo><mn mathvariant="italic">5</mn></math> wavelengths for MP3</span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">«</span><span class="fontstyle1">equally spaced</span><span class="fontstyle0">» </span><span class="fontstyle1">maxima and minima </span><span class="fontstyle3">✓</span></p>
<p><span class="fontstyle1">a maximum at Q </span><span class="fontstyle3">✓</span></p>
<p><span class="fontstyle1">four </span><span class="fontstyle0">«</span><span class="fontstyle1">additional</span><span class="fontstyle0">» </span><span class="fontstyle1">maxima </span><span class="fontstyle0">«</span><span class="fontstyle1">between P and Q</span><span class="fontstyle0">» </span><span class="fontstyle3">✓</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">the amplitude of sound at Q is halved </span><span class="fontstyle2">✓<br></span><span class="fontstyle3">«</span><span class="fontstyle0">intensity is proportional to amplitude squared hence</span><span class="fontstyle3">» <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>I</mi><mi mathvariant="normal">A</mi></msub><msub><mi>I</mi><mn>0</mn></msub></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac></math> </span><span class="fontstyle2">✓</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">speed of sound relative to the microphone is less </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle2"><br></span><span class="fontstyle0">wavelength unchanged </span><span class="fontstyle3">«</span><span class="fontstyle0">so frequency is lower</span><span class="fontstyle3">»<br></span><span class="fontstyle4"><em><strong>OR</strong></em><br></span><span class="fontstyle0">fewer waves recorded in unit time/per second </span><span class="fontstyle3">«</span><span class="fontstyle0">so frequency is lower</span><span class="fontstyle3">» </span><span class="fontstyle2">✓</span></p>
<div class="question_part_label">d(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>845</mn><mo>=</mo><mn>850</mn><mo>×</mo><mfrac><mrow><mn>340</mn><mo>-</mo><mi>v</mi></mrow><mn>340</mn></mfrac></math> ✓</span></p>
<p> </p>
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>00</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> ✓</span></p>
<div class="question_part_label">d(ii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This was answered very well, with those not scoring full marks able to, at least, calculate the wavelength.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most candidates were able to score at least one mark by referring to a maximum at Q.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most candidates earned 2 marks or nothing. A common answer was that intensity was 1/2 the original.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>HL only. The majority of candidates answered this by describing the Doppler Effect for a moving source. Others reworded the question without adding any explanation. Correct explanations were rare.</p>
<div class="question_part_label">d(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>HL only. This was answered well with the majority of candidates able to identify the correct formula and the correct values to substitute.</p>
<div class="question_part_label">d(ii).</div>
</div>
<br><hr><br><div class="specification">
<p>There is a proposal to place a satellite in orbit around planet Mars.</p>
</div>

<div class="specification">
<p>The satellite is to have an orbital time <em>T</em> equal to the length of a day on Mars. It can&nbsp;be shown that</p>
<p style="text-align: center;"><em>T</em><sup>2</sup> = <em>kR</em><sup>3</sup></p>
<p>where<em> R</em> is the orbital radius of the satellite and <em>k</em> is a constant.</p>
</div>

<div class="specification">
<p>The ratio&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{distance of Mars from the Sun}}}}{{{\text{distance of Earth from the Sun}}}}">
  <mfrac>
    <mrow>
      <mrow>
        <mtext>distance of Mars from the Sun</mtext>
      </mrow>
    </mrow>
    <mrow>
      <mrow>
        <mtext>distance of Earth from the Sun</mtext>
      </mrow>
    </mrow>
  </mfrac>
</math></span> = 1.5.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline what is meant by gravitational field strength at a point.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Newton’s law of gravitation applies to point masses. Suggest why the law can be applied to a satellite orbiting Mars.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Mars has a mass of 6.4 × 10<sup>23</sup> kg. Show that, for Mars, <em>k</em> is about 9 × 10<sup>–13 </sup>s<sup>2 </sup>m<sup>–3</sup>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The time taken for Mars to revolve on its axis is 8.9 × 10<sup>4</sup> s. Calculate, in m s<sup>–1</sup>, the orbital speed of the satellite.</p>
<p> </p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the intensity of solar radiation at the orbit of Mars is about 600 W m<sup>–2</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine, in K, the mean surface temperature of Mars. Assume that Mars acts as a black body.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The atmosphere of Mars is composed mainly of carbon dioxide and has a pressure less than 1 % of that on the Earth. Outline why the mean temperature of Earth is strongly affected by gases in its atmosphere but that of Mars is not.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>force per unit mass ✔</p>
<p>acting on a small/test/point mass «placed at the point in the field» ✔</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Mars is spherical/a sphere «and of uniform density so behaves as a point mass» ✔</p>
<p>satellite has a much smaller mass/diameter/size than Mars «so approximates to a point mass» ✔</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{m{v^2}}}{r} = \frac{{GMm}}{{{r^2}}}">
  <mfrac>
    <mrow>
      <mi>m</mi>
      <mrow>
        <msup>
          <mi>v</mi>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
    <mi>r</mi>
  </mfrac>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mi>G</mi>
      <mi>M</mi>
      <mi>m</mi>
    </mrow>
    <mrow>
      <mrow>
        <msup>
          <mi>r</mi>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
</math></span> hence» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = \sqrt {\frac{{GM}}{R}} ">
  <mi>v</mi>
  <mo>=</mo>
  <msqrt>
    <mfrac>
      <mrow>
        <mi>G</mi>
        <mi>M</mi>
      </mrow>
      <mi>R</mi>
    </mfrac>
  </msqrt>
</math></span>. Also <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = \frac{{2\pi R}}{T}">
  <mi>v</mi>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>2</mn>
      <mi>π</mi>
      <mi>R</mi>
    </mrow>
    <mi>T</mi>
  </mfrac>
</math></span></p>
<p><em><strong>OR</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m{\omega ^2}r = \frac{{GMm}}{{{r^2}}}">
  <mi>m</mi>
  <mrow>
    <msup>
      <mi>ω</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mi>r</mi>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mi>G</mi>
      <mi>M</mi>
      <mi>m</mi>
    </mrow>
    <mrow>
      <mrow>
        <msup>
          <mi>r</mi>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
</math></span> hence <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\omega ^2} = \frac{{GM}}{{{R^3}}}">
  <mrow>
    <msup>
      <mi>ω</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mi>G</mi>
      <mi>M</mi>
    </mrow>
    <mrow>
      <mrow>
        <msup>
          <mi>R</mi>
          <mn>3</mn>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
</math></span> ✔</p>
<p> </p>
<p>uses either of the above to get <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{T^2} = \frac{{4{\pi ^2}}}{{GM}}{R^3}">
  <mrow>
    <msup>
      <mi>T</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>4</mn>
      <mrow>
        <msup>
          <mi>π</mi>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mi>G</mi>
      <mi>M</mi>
    </mrow>
  </mfrac>
  <mrow>
    <msup>
      <mi>R</mi>
      <mn>3</mn>
    </msup>
  </mrow>
</math></span></p>
<p><em><strong>OR</strong></em></p>
<p>uses <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = \frac{{4{\pi ^2}}}{{GM}}">
  <mi>k</mi>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>4</mn>
      <mrow>
        <msup>
          <mi>π</mi>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mi>G</mi>
      <mi>M</mi>
    </mrow>
  </mfrac>
</math></span> ✔</p>
<p> </p>
<p><em>k</em> = 9.2 × 10<sup>−13</sup> / 9.3 × 10<sup>−13</sup></p>
<p> </p>
<p> </p>
<p><em>Unit not required</em></p>
<p> </p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{R^3} = \frac{{{T^2}}}{k} = \frac{{{{\left( {8.9 \times {{10}^4}} \right)}^2}}}{{9.25 \times {{10}^{ - 13}}}}">
  <mrow>
    <msup>
      <mi>R</mi>
      <mn>3</mn>
    </msup>
  </mrow>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mrow>
        <msup>
          <mi>T</mi>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
    <mi>k</mi>
  </mfrac>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mrow>
        <msup>
          <mrow>
            <mrow>
              <mo>(</mo>
              <mrow>
                <mn>8.9</mn>
                <mo>×</mo>
                <mrow>
                  <msup>
                    <mrow>
                      <mn>10</mn>
                    </mrow>
                    <mn>4</mn>
                  </msup>
                </mrow>
              </mrow>
              <mo>)</mo>
            </mrow>
          </mrow>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mn>9.25</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>13</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
</math></span>  <em>R</em> = 2.04 × 10<sup>7</sup> «m» ✔</p>
<p> </p>
<p><em>v</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\omega r = \frac{{2\pi  \times 2.04 \times {{10}^7}}}{{89000}} = ">
  <mi>ω</mi>
  <mi>r</mi>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>2</mn>
      <mi>π</mi>
      <mo>×</mo>
      <mn>2.04</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mn>7</mn>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mn>89000</mn>
    </mrow>
  </mfrac>
  <mo>=</mo>
</math></span>» 1.4 × 10<sup>3</sup> «m s<sup>–1</sup>»</p>
<p><em><strong>OR</strong></em></p>
<p><em>v</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{GM}}{R}}  = \sqrt {\frac{{6.67 \times {{10}^{ - 11}} \times 6.4 \times {{10}^{23}}}}{{2.04 \times {{10}^7}}}}  = ">
  <msqrt>
    <mfrac>
      <mrow>
        <mi>G</mi>
        <mi>M</mi>
      </mrow>
      <mi>R</mi>
    </mfrac>
  </msqrt>
  <mo>=</mo>
  <msqrt>
    <mfrac>
      <mrow>
        <mn>6.67</mn>
        <mo>×</mo>
        <mrow>
          <msup>
            <mrow>
              <mn>10</mn>
            </mrow>
            <mrow>
              <mo>−</mo>
              <mn>11</mn>
            </mrow>
          </msup>
        </mrow>
        <mo>×</mo>
        <mn>6.4</mn>
        <mo>×</mo>
        <mrow>
          <msup>
            <mrow>
              <mn>10</mn>
            </mrow>
            <mrow>
              <mn>23</mn>
            </mrow>
          </msup>
        </mrow>
      </mrow>
      <mrow>
        <mn>2.04</mn>
        <mo>×</mo>
        <mrow>
          <msup>
            <mrow>
              <mn>10</mn>
            </mrow>
            <mn>7</mn>
          </msup>
        </mrow>
      </mrow>
    </mfrac>
  </msqrt>
  <mo>=</mo>
</math></span>» 1.4 × 10<sup>3</sup> «m s<sup>–1</sup>» ✔</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="I \propto \frac{1}{{{r^2}}}">
  <mi>I</mi>
  <mo>∝</mo>
  <mfrac>
    <mn>1</mn>
    <mrow>
      <mrow>
        <msup>
          <mi>r</mi>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
</math></span> «1.36 × 10<sup>3</sup> × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{{{1.5}^2}}}">
  <mfrac>
    <mn>1</mn>
    <mrow>
      <mrow>
        <msup>
          <mrow>
            <mn>1.5</mn>
          </mrow>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
</math></span>» ✔</p>
<p>604 «W m<sup>–2</sup>» ✔</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{600}}{4}">
  <mfrac>
    <mrow>
      <mn>600</mn>
    </mrow>
    <mn>4</mn>
  </mfrac>
</math></span> for mean intensity ✔</p>
<p>temperature/K = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt[4]{{\frac{{600}}{{4 \times 5.67 \times {{10}^{ - 8}}}}}} = ">
  <mroot>
    <mrow>
      <mfrac>
        <mrow>
          <mn>600</mn>
        </mrow>
        <mrow>
          <mn>4</mn>
          <mo>×</mo>
          <mn>5.67</mn>
          <mo>×</mo>
          <mrow>
            <msup>
              <mrow>
                <mn>10</mn>
              </mrow>
              <mrow>
                <mo>−</mo>
                <mn>8</mn>
              </mrow>
            </msup>
          </mrow>
        </mrow>
      </mfrac>
    </mrow>
    <mn>4</mn>
  </mroot>
  <mo>=</mo>
</math></span>» 230 ✔</p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>reference to greenhouse gas/effect ✔</p>
<p>recognize the link between molecular density/concentration and pressure ✔</p>
<p>low pressure means too few molecules to produce a significant heating effect</p>
<p><em><strong>OR</strong></em></p>
<p>low pressure means too little radiation re-radiated back to Mars ✔</p>
<p> </p>
<p><em>The greenhouse effect can be described, it doesn’t have to be named</em></p>
<div class="question_part_label">c.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>A beam of microwaves is incident normally on a pair of identical narrow slits S1 and S2.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">When a microwave receiver is initially placed at W which is equidistant from the slits, a maximum in intensity is observed. The receiver is then moved towards Z along a line parallel to the slits. Intensity maxima are observed at X and Y with one minimum between them. W, X and Y are consecutive maxima.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why intensity maxima are observed at X and Y.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The distance from S1 to Y is 1.243 m and the distance from S2 to Y is 1.181 m.</p>
<p>Determine the frequency of the microwaves.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline <strong>one</strong> reason why the maxima observed at W, X and Y will have different intensities from each other.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The microwaves emitted by the transmitter are horizontally polarized. The microwave receiver contains a polarizing filter. When the receiver is at position W it detects a maximum intensity.</p>
<p style="text-align:center;"><img 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"></p>
<p style="text-align:left;">The receiver is then rotated through 180° about the horizontal dotted line passing through the microwave transmitter. Sketch a graph on the axes provided to show the variation of received intensity with rotation angle.</p>
<p style="text-align:left;"><img style="display:block;margin-left:auto;margin-right:auto;" 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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>two waves superpose/mention of superposition/mention of «constructive» interference ✔</p>
<p>they arrive in phase/there is a path length difference of an integer number of wavelengths ✔</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>path difference = 0.062 «m»✔</p>
<p>so wavelength = 0.031 «m»✔</p>
<p>frequency = 9.7 × 10<sup>9</sup> «Hz»✔</p>
<p><em>Award <strong>[2 max]</strong> for 4.8 x 10<sup>9</sup> Hz</em>.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>intensity is modulated by a single slit diffraction envelope <em><strong>OR</strong></em></p>
<p>intensity varies with distance <em><strong>OR</strong></em> points are different distances from the slits ✔<br><br></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img 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"></p>
<p>cos<sup>2</sup> variation shown ✔</p>
<p>with zero at 90° (by eye) ✔</p>
<p><em>Award <strong>[1 max]</strong> for an inverted curve with maximum at 90°.</em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Many candidates were able to discuss the interference that is taking place in this question, but few were able to fully describe the path length difference. That said, the quality of responses on this type of question seems to have improved over the last few examination sessions with very few candidates simply discussing the crests and troughs of waves.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates struggled with this question. Few were able to calculate a proper path length difference, and then use that to calculate the wavelength and frequency. Many candidates went down blind paths of trying various equations from the data booklet, and some seemed to believe that the wavelength is just the reciprocal of the frequency.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This is one of many questions on this paper where candidates wrote vague answers that did not clearly connect to physics concepts or include key information. There were many overly simplistic answers like “they are farther away” without specifying what they are farther away from. Candidates should be reminded that their responses should go beyond the obvious and include some evidence of deeper understanding.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was generally well answered, with many candidates at least recognizing that the intensity would decrease to zero at 90 degrees. Many struggled with the exact shape of the graph, though, and some drew a graph that extended below zero showing a lack of understanding of what was being graphed.</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The ball is now displaced through a small distance <em>x </em>from the bottom of the bowl and is&nbsp;then released from rest.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-14_om_06.19.20.png" alt="M18/4/PHYSI/HP2/ENG/TZ2/01.d"></p>
<p>The magnitude of the force on the ball towards the equilibrium position is given by</p>
<p style="text-align: left;"><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\frac{{mgx}}{R}">
  <mfrac>
    <mrow>
      <mi>m</mi>
      <mi>g</mi>
      <mi>x</mi>
    </mrow>
    <mi>R</mi>
  </mfrac>
</math></span></p>
<p>where <em>R </em>is the radius of the bowl.</p>
</div>

<div class="specification">
<p>A small ball of mass <em>m </em>is moving in a horizontal circle on the inside surface of a&nbsp;frictionless hemispherical bowl.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-12_om_12.45.38.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/01.a"></p>
<p>The normal reaction force <em>N </em>makes an angle <em>θ</em> to the horizontal.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the direction of the resultant force on the ball.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the diagram, construct an arrow of the correct length to represent the&nbsp;weight of the ball.</p>
<p><img 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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the magnitude of the net force <em>F </em>on the ball is given by the following&nbsp;equation.</p>
<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="F = \frac{{mg}}{{\tan \theta }}">
  <mi>F</mi>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mi>m</mi>
      <mi>g</mi>
    </mrow>
    <mrow>
      <mi>tan</mi>
      <mo>⁡</mo>
      <mi>θ</mi>
    </mrow>
  </mfrac>
</math></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The radius of the bowl is 8.0 m and <em>θ</em> = 22°. Determine the speed of the ball.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline whether this ball can move on a horizontal circular path of radius equal to the&nbsp;radius of the bowl.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the ball will perform simple harmonic oscillations about the&nbsp;equilibrium position.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the period of oscillation of the ball is about 6 s.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The amplitude of oscillation is 0.12 m. On the axes, draw a graph to show the&nbsp;variation with time <em>t </em>of the velocity <strong><em>v </em></strong>of the ball during one period.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A second identical ball is placed at the bottom of the bowl and the first ball is displaced&nbsp;so that its height from the horizontal is equal to 8.0 m.</p>
<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<img src="images/Schermafbeelding_2018-08-12_om_13.41.19.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/01.d"></p>
<p>The first ball is released and eventually strikes the second ball. The two balls remain&nbsp;in contact. Determine, in m, the maximum height reached by the two balls.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>towards the centre <strong>«</strong>of the circle<strong>» </strong>/ horizontally to the right</p>
<p>&nbsp;</p>
<p><em>Do not accept towards the centre of the bowl</em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>downward vertical arrow of any length</p>
<p>arrow of correct length</p>
<p>&nbsp;</p>
<p><em>Judge the length of the vertical arrow by eye. The construction lines are not required. A label is not required</em></p>
<p><em>eg</em>:&nbsp;<img src="images/Schermafbeelding_2018-08-12_om_13.22.33.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/01.a.ii"></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><em>ALTERNATIVE 1</em></strong></p>
<p><em>F</em> = <em>N</em>&nbsp;cos&nbsp;<em>θ</em></p>
<p><em>mg</em> =&nbsp;<em>N</em> sin&nbsp;<em>θ</em></p>
<p>dividing/substituting to get result</p>
<p>&nbsp;</p>
<p><strong><em>ALTERNATIVE 2</em></strong></p>
<p>right angle triangle drawn with <em>F</em>, <em>N </em>and <em>W/mg </em>labelled</p>
<p>angle correctly labelled and arrows on forces in correct directions</p>
<p>correct use of trigonometry leading to the required relationship</p>
<p>&nbsp;</p>
<p><img src="images/Schermafbeelding_2018-08-12_om_13.28.39.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/01.a.ii"></p>
<p><em>tan&nbsp;θ</em> =&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\text{O}}}{A} = \frac{{mg}}{F}">
  <mfrac>
    <mrow>
      <mtext>O</mtext>
    </mrow>
    <mi>A</mi>
  </mfrac>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mi>m</mi>
      <mi>g</mi>
    </mrow>
    <mi>F</mi>
  </mfrac>
</math></span></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{mg}}{{\tan \theta }}">
  <mfrac>
    <mrow>
      <mi>m</mi>
      <mi>g</mi>
    </mrow>
    <mrow>
      <mi>tan</mi>
      <mo>⁡</mo>
      <mi>θ</mi>
    </mrow>
  </mfrac>
</math></span> =&nbsp;<em>m</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{v^2}}}{r}">
  <mfrac>
    <mrow>
      <mrow>
        <msup>
          <mi>v</mi>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
    <mi>r</mi>
  </mfrac>
</math></span></p>
<p><em>r</em> = <em>R</em> cos&nbsp;<em>θ</em></p>
<p><em>v</em> =&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{gR{{\cos }^2}\theta }}{{\sin \theta }}} /\sqrt {\frac{{gR\cos \theta }}{{\tan \theta }}} /\sqrt {\frac{{9.81 \times 8.0\cos 22}}{{\tan 22}}} ">
  <msqrt>
    <mfrac>
      <mrow>
        <mi>g</mi>
        <mi>R</mi>
        <mrow>
          <msup>
            <mrow>
              <mi>cos</mi>
            </mrow>
            <mn>2</mn>
          </msup>
        </mrow>
        <mi>θ</mi>
      </mrow>
      <mrow>
        <mi>sin</mi>
        <mo>⁡</mo>
        <mi>θ</mi>
      </mrow>
    </mfrac>
  </msqrt>
  <mrow>
    <mo>/</mo>
  </mrow>
  <msqrt>
    <mfrac>
      <mrow>
        <mi>g</mi>
        <mi>R</mi>
        <mi>cos</mi>
        <mo>⁡</mo>
        <mi>θ</mi>
      </mrow>
      <mrow>
        <mi>tan</mi>
        <mo>⁡</mo>
        <mi>θ</mi>
      </mrow>
    </mfrac>
  </msqrt>
  <mrow>
    <mo>/</mo>
  </mrow>
  <msqrt>
    <mfrac>
      <mrow>
        <mn>9.81</mn>
        <mo>×</mo>
        <mn>8.0</mn>
        <mi>cos</mi>
        <mo>⁡</mo>
        <mn>22</mn>
      </mrow>
      <mrow>
        <mi>tan</mi>
        <mo>⁡</mo>
        <mn>22</mn>
      </mrow>
    </mfrac>
  </msqrt>
</math></span></p>
<p><em>v</em> = 13.4/13&nbsp;<strong>«</strong><em>ms&nbsp;<sup>–</sup></em><em><sup>1</sup></em><strong>»</strong></p>
<p>&nbsp;</p>
<p><em>Award </em><strong><em>[4] </em></strong><em>for a bald correct answer&nbsp;</em></p>
<p><em>Award </em><strong><em>[3] </em></strong><em>for an answer of 13.9/14 </em><strong>«</strong><em>ms&nbsp;<sup>–</sup></em><em><sup>1</sup></em><strong>»</strong><em>. MP2 omitted</em></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>there is no force to balance the weight/N is horizontal</p>
<p>so no / it is not possible</p>
<p>&nbsp;</p>
<p><em>Must see correct justification to award MP2</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the <strong>«</strong>restoring<strong>» </strong>force/acceleration is proportional to displacement</p>
<p>&nbsp;</p>
<p><em>Direction is not required</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>ω</em> =&nbsp;<strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{g}{R}} ">
  <msqrt>
    <mfrac>
      <mi>g</mi>
      <mi>R</mi>
    </mfrac>
  </msqrt>
</math></span><strong>»</strong> =&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{9.81}}{{8.0}}} ">
  <msqrt>
    <mfrac>
      <mrow>
        <mn>9.81</mn>
      </mrow>
      <mrow>
        <mn>8.0</mn>
      </mrow>
    </mfrac>
  </msqrt>
</math></span>&nbsp;<strong>«</strong>= 1.107 s<sup>–1</sup><strong>»</strong></p>
<p><em>T</em> =&nbsp;<strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2\pi }}{\omega }">
  <mfrac>
    <mrow>
      <mn>2</mn>
      <mi>π</mi>
    </mrow>
    <mi>ω</mi>
  </mfrac>
</math></span> =&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2\pi }}{{1.107}}">
  <mfrac>
    <mrow>
      <mn>2</mn>
      <mi>π</mi>
    </mrow>
    <mrow>
      <mn>1.107</mn>
    </mrow>
  </mfrac>
</math></span> =<strong>»</strong> 5.7&nbsp;<strong>«</strong>s<strong>»</strong></p>
<p>&nbsp;</p>
<p><em>Allow use of </em>or <em>g&nbsp;= 9.8 or 10</em></p>
<p><em>Award </em><strong><em>[0] </em></strong><em>for a substitution into T = 2π</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{I}{g}} ">
  <msqrt>
    <mfrac>
      <mi>I</mi>
      <mi>g</mi>
    </mfrac>
  </msqrt>
</math></span></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>sine graph</p>
<p>correct amplitude <strong>«</strong>0.13 m s<sup>–1</sup><strong>»</strong></p>
<p>correct period and only 1 period shown</p>
<p>&nbsp;</p>
<p><em>Accept ± sine for shape of the graph. Accept 5.7 s or 6.0 s for the correct period.</em></p>
<p><em>Amplitude should be correct to ±</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
  <mfrac>
    <mn>1</mn>
    <mn>2</mn>
  </mfrac>
</math></span>&nbsp;<em>square for MP2</em></p>
<p><em>eg: v /</em>m s<sup>–1&nbsp;&nbsp;</sup>&nbsp;<img src="images/Schermafbeelding_2018-08-14_om_06.59.06.png" alt="M18/4/PHYSI/HP2/ENG/TZ2/01.d.iii"></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>speed before collision&nbsp;<em>v</em> = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {2gR} "> <msqrt> <mn>2</mn> <mi>g</mi> <mi>R</mi> </msqrt> </math></span> =<strong>»</strong> 12.5&nbsp;<strong>«</strong>ms<sup>–1</sup><strong>»</strong></p>
<p><strong>«</strong>from conservation of momentum<strong>» </strong>common speed after collision is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math></span>&nbsp;initial speed&nbsp;<strong>«</strong><em>v<sub>c</sub></em> =&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{12.5}}{2}"> <mfrac> <mrow> <mn>12.5</mn> </mrow> <mn>2</mn> </mfrac> </math></span> = 6.25 ms<sup>–1</sup><strong>»</strong></p>
<p><em>h =&nbsp;</em><strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{v_c}^2}}{{2g}} = \frac{{{{6.25}^2}}}{{2 \times 9.81}}"> <mfrac> <mrow> <msup> <mrow> <msub> <mi>v</mi> <mi>c</mi> </msub> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <mi>g</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <msup> <mrow> <mn>6.25</mn> </mrow> <mn>2</mn> </msup> </mrow> </mrow> <mrow> <mn>2</mn> <mo>×</mo> <mn>9.81</mn> </mrow> </mfrac> </math></span><strong>»</strong> 2.0&nbsp;<strong>«</strong>m<strong>»</strong></p>
<p>&nbsp;</p>
<p><em>Allow 12.5 from incorrect use of kinematics equations</em></p>
<p><em>Award </em><strong><em>[3] </em></strong><em>for a bald correct answer</em></p>
<p><em>Award </em><strong><em>[0] </em></strong><em>for mg(8)&nbsp;=&nbsp;2mgh leading to h = 4 m if done in one step.</em></p>
<p><em>Allow ECF from MP1</em></p>
<p><em>Allow ECF from MP2</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A student investigates how light can be used to measure the speed of a toy train.</p>
<p style="text-align: center;"><img 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"><img src="blob:https://questionbank.ibo.org/55ba542d-3306-4ee7-8386-825edadb928d"></p>
<p>Light from a laser is incident on a double slit. The light from the slits is detected by a&nbsp;light sensor attached to the train.</p>
<p>The graph shows the variation with time of the output voltage from the light sensor as&nbsp;the train moves parallel to the slits. The output voltage is proportional to the intensity of&nbsp;light incident on the sensor.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: center;"><img src="blob:https://questionbank.ibo.org/4e0f3fdc-c845-43ef-ba7c-39bab20625cf"></p>
<p>&nbsp;</p>
</div>

<div class="specification">
<p>As the train continues to move, the first diffraction minimum is observed when the&nbsp;light sensor is at a distance of 0.13 m from the centre of the fringe pattern.</p>
<p style="text-align: center;"><img 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"></p>
</div>

<div class="specification">
<p>A student investigates how light can be used to measure the speed of a toy train.</p>
<p style="text-align: center;"><img 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NAJrT9LpwAFKEABClAgiAIMdIKIy6wpQAEKUIACFAitAAOd0PqzdApQgAIUoAAFgijAQCeIuMyaAhSgAAUoQIHQCjDQCa0/S6cABShAAQpQIIgCDHSCiMusKUABClCAAhQIrQADndD6s3QKUIACFKAABYIowEAniLjMmgIUoAAFKECB0ArIrFarNbRVYOkUoEA4CshkMvT158NgMODatWs4f/48rl+/joMHD2LOnDkYMWIEpkyZgltuuQXx8fFem+9PGV5P5hsUoAAFADDQ4ceAAhQYkICnIEQEM42NjaiursZrr72Gn/3sZ/inf/onqNVqlzJEuk8//RRffPEF/vjHP2LVqlVS2mnTprmk81SGSwK+oAAFKNCHAAOdPoD4NgUo4FnAPQh54403sG7dOkydOhUpKSmYMGGCNHLj+eyeo1evXsXFixfx7rvvwmKxYPPmzVIeIoV7GT1n8RkFKEAB/wQY6PjnxFQUoICbgHMQsnPnTtTV1WHevHm49dZb3VL6//Jvf/sbXnrpJdTU1EjBknMZ/ufClBSgAAV6BBjo9FjwGQUo0A8BRxBy+fJl/PSnP8XTTz/t1whOX0UYjUZpLU9DQwNHdPrC4vsUoECfAgx0+iRiAgpQwCEggptQP/paAB3q+rF8ClBgeAl8a3hVh7WhAAWGu0AoA43hEGgN9/5h/ShAAVcB7qPj6sFXFKAABShAAQpEkAADnQjqTDaFAhSgAAUoQAFXAQY6rh58RQEKUIACFKBABAkw0AlaZ1rQqSuDSjYPWsONwJZiaYM2JwE52jZYvOZ8AwbtPMhytDB4T+T1bP/fcC/H/lpVBl2nKNgCs6EelWX7glwP/2vMlBSgAAUoED0CDHSip6+HqKUjkVh4AFbjRmTGio/XZTRVrcbKlgAHe0PUGhZDAQpQgALhLcBAJ7z7j7WnAAUoQAEKUMCHAAMdHzj9estiQktdJQpUMmmTM1XBFhw5fdEtCzGNo4NWkyOlkclUyNBooTN02tM5prtSodFdcjr3EnSaVMi6p4Psb10+i6OVBVDJRJnJKKish8Hsa57qJkwt1dBkqOzl50Cj1fVxjnudZZBlaKDVGWB2qmHPU+epq39Ap3kQWZtagIYiqGPc29VzFp9RgAIUoAAFgiHAQCcgqlfQsmUxUrdfxqzGr2C1dsGwehJOv30Upu78LTC3VWNJeglOxD0FY5cV1q4WVMSdwEL1AlS2XOlO6d+Ta2hYuQ77Yh5Di8jr6huY9fkWqGduRYvHYOcmLtYtR8rMY4iraEGXVZzzO6hPlCC95CAueouPzM14sbgUJ9S/w1VxjvVrGNfeguqsNTjQ59qjcciseAfHS1OA7Crou5pRkTnOv+YxFQUoQAEKUCAAAgx0AoCIztM4sKUDpWuXIy8xFoAcisTZWL12EZTd+V9G0yvbcTR3HTaWTINSyMuVSHvid6gp7cDKsrp+L9ZVFjrlpUhC3moNSvWv4kDT5e5Su590nsS2pXVILl+FkjQlpI5XTEHh9q3IP7IR2xqdR5C6z4LFeBZHGydhxvQEKKTDI6DMfBrvWg+gMHFkT0I+owAFKEABCgxDAQY6g+4UCzqbj6HaNAnqeFsoYMtSDkV8ApId+Xf+FfXVRiRPu9MW5DiOQ4F49SSg9RzaPY7EdCd0e3JL77wUKqiTjaiu/ysck2G2kxx1VGHqxHG2IMeRm9dzbAnkqil4IP0k1lS9hSbdW07TbI4M+JsCfQucOXMGr776Kvbu3Qtxl/P29va+T2IKClCAAgEQYKAzaMSb6LhwzmmKynOGlo4LONMzj9U7kekcLnTc7H08oEdasClrvH19jm0tkSxmMooafFRMkYYVhxtRc8+XqF3/GLLU34VM5s/anoBWnJmFqUBLSwvuuusuaDQatLa24qOPPsLJkycxf/58LFiwgAFPmPYrq02BcBLgva4G3VsjEDcxAUqc85mTPG4ipiqBM95SKRMwMW4EENR/6M5FlX5v/6ecFInIzBM/i1EhFl0ffBXblmYhXX8cbRU/8dYiHo9yATFy89RTT2HZsmVQqVQuGhkZGRCjPLfddhv+8pe/YOrUqS7v8wUFKECBQAlwRGfQknLEpt6PfOV56Nudr0OywNx+Dq2O/GPvQk6+Cq2nPoLJZeGvGe3680ByAuIV33Kd7nKc6/H3NbTqja5XPpmN0LeqkJ9zF8RKoZ6Ho44f49TZz1w3GTQ3oTKjr80He3IS64pS8hahID8FpjMX0OHSFqd0fBrVAmIkRwQ5K1as6BXkOGBEcPPMM89g4cKFuHzZw7oyR0L+pgAFKDAIAQY6g8DrPjV2Oh7fcS+qF2qgbROrY8Ql2QexYf1upymtsUh7dBkeOPI0yraesgc7nWjTarBwUxw2b8xDohyQJ/wE87ONqN7zNtqkNTudMNRtwXpxibbbw7SpAhvq2mzBjvkstMtKUJ1bhsfTPVzZJNVxBo4sfQpbm0y2YMfchrr1a7ESS7BxXqLr2h17WRaDFjliqspRjtS291DfBBQWZyGhz0+QfQ2SlN8NmM3fuLWCLyNR4Mknn0RBQQFuvfVWn81LSkpCVlYWXn75ZZ/pwuPNThiObkPZHl87lgeqJYEsy3lLCP7LJVA9xHyGj0CfX1PDp6rDuSYjMCFvIxr3TMGJTLGGJQaji5vx42WPI7u72nIokvLxfONWzOj4LVQxYo1MEn6tn4Ya/T6sSBljSylPxLztr2A5KjF5dAxksrmoupqNtS/N7c7J9uQWZG9ejMzzzyBR7KMz+t9xIrkSjVtnY4LHXrXXsWYGOjQpiJHOmYtD44vRvG8JUhQeT4I8cSF2Nxdj/KG5GC3t1xOD0emHMH7ZTpTPvsNjcORa0ZFIyF2MVTfXQB0zCXMOnHMdUXJNzFcRICCmpK5duwYRxPjzSE1NldbwXL9+3Z/kwzdNZzOqCp5FS9cQVDGgZbnvZj4E9WcRFBhCAZnVarUOYXksigIUCGMBmUyGvv5kvP7663j//fch1uH4+6ipqcHGjRuRmJjo8xR/yveZQTDf7NRBk7QQZ8p1OFKY5Mc/AgZRmaEsaxDV5KkUGA4Cnv8ZPxxqxjpQgAJhKfDpp59CqezZQcqfRowdOxYXLlzwJ+nwTCMFHlnYZDKhoWgyYrp3MXffWdx1N3TLxToUqTztGG7bDV2l0bltFQHAY1liF/JUadfyXY7d0h11cNu1vfeO7G5TVyJ/lQo5u46iaY8GGdJIrgyqgudwtHsX9+HZDawVBTwJMNDxpMJjFKDAoARu3Iiym7jGZqKi7ThKlUpkV32MLummtuhzN3T5hPvwcD5Q/ep7rruTS/tuwcOFBQA8lmX/U974B5wcuxIGsYN5YzHSYjulXdtnHhqFJS1fS6Nx1q4/Y23MfmQVV3nZRV10vQkNj1WidvSjOCx2RO9qR82Ed5Dt85xBfWR4MgWCJsBAJ2i0zJgC0Slw++2348svv+xX48UGghMnTuzXOcM/sT+7oY9F2ryHoda+jvpzjuDQvsEnspGTOrZ/zVTORMFDd0KBEVAm3gGFfdf2/IL5SFOOsOUln4D0RfOR3fg+PjR637tLWarB6rwk247ociVS70+Bso9z+ldZpqbA0Agw0BkaZ5ZCgagRmD59Opqbm/1u79WrV3HkyBFpTx2/TwqHhH7thg4ofpSL/OzT2H/ygn2h/mU01zcA+fcjNXaQf6LF6I+xGRVpl6Grq0Od+NFqkKUuQkO/DB07vbtvo9GvTJiYAiERGOT/RSGpMwulAAWGsUB8fDxGjx4tbQjoTzXr6+tRUVGBUaNG+ZM8bNL4vRu6fBJyih9E65q9aOy0AFKAFIfl8+522w9rIE0XW1gUQTVajaztf4J06+AxuXih+SVkg0HLQER5TvgJcGfk8Osz1pgCw15g27ZtmDVrljRK42svnba2Nnz44YfYtWvXsG+T2NRQjFQdO3YMjz/+OERA5+vh927okGPC/XnIRynqm3+DVBxDdXIeGn9k33LCVyF9vGcxvImSoibk1l7ArjzHdhAWdOoapM1MuR91H4B8OyIEOKITEd3YuxFhvydJ7ybxSBgJiMvEd+7cicrKSo8jOzdv3sS7774LcVm5mLYarqM5IrhpaGjA4sWL8eCDD8JgMEj36OoryJG6yq/d0O1/gmPvxrzlcah+9XXsf/sEkuf/xI/NOPv6QDh2Z5+MaVO+73S5+ze4esX1tr995cT3KRDOAhzRCefe81F38eWhUCiQnd2zZaGP5HyLAgEXuO+++3Do0CFp9OP48eOYPHkyxGXkYuGxuL+V2Gfnvffek44FvPBBZCjqJ24+Ku7VJUabHnnkESxZsqTv+3EpVFAn32K7n901M8wj7buhZ4rd0L+PZ0umQSl32g292bYbuq2qY/CjX+QheWURHoO4J91Ep8DEQ2N6leUhDRy3ftmN6t1/RG75A1DKb8LUtAtlS5+HCSmeTuIxCkScAAOdiOvSngaZzc733uo5zmcUGCoBMbLzzjvvSMGNCB7EZ3LmzJndQc9Q1aOvckRwo9PppMW6RqPR/+DGOWP5JORq8lGdNRkxRfYb6Eq7od+GA1ViN3Sx/FeJ9NJy1OgfQmai2x3pErJQXDgFDe0PYnrCSOecez/vVdbv4PGatdjp+M3hCvzXigKoYkwApuCRzWtQcPANxM1+tne+PEKBCBTgzsgR2KmiSeLqCvHIy8uL0BayWaEQCPXOxIEs31NwI64YC9md1C1t0OYuxKniWqf1NKHoZZZJgcgS4IhOZPUnW0MBCvgQ8BTc/Od//mfogpvuut6EqXE/qm8+jMrs23xPW3WfwycUoIA/Agx0/FFiGgpQIGwFnIMb0Qgxyrlp06Y+76s1VA22GLTIFfvapK9C7c4irzfYHar6sBwKRJoAA51I61G2hwIUkK6O+uCDD1ymcHfs2NHnJeGhoJMnFqLeWhiKolkmBaJCgIFOVHQzG0mByBc4c+YMTp48ib1790KlUkkjN8M1uIn83mALKTB8BBjoDJ++YE0oQIF+CngKbsRCfL/2uelnWUxOAQqEpwADnfDsN9aaAlErwOAmarueDafAgAQY6AyIjSdRgAJDKeAIbkSZzz//PObOnSvtzyM2IOSDAhSggC8BBjq+dPgeBSgQEgFxC5PTp09LOyiLNTc//OEPpeBGVCYc7osVEjQWSgEKeBRgoOORhQcpQIFQCuj1euzevZsjN6HsBJZNgQgRYKATIR3JZlAgkgTE7sQcuYmkHmVbKBA6Ad69PHT2LJkCFKAABShAgSALMNAJMjCzpwAFKEABClAgdAIMdEJnH9KSxc0R+aAABShAAQpEugADnUjvYbaPAhSgAAUoEMUCDHSiuPPZdApQgAIUoECkCzDQifQeZvsoQAEKUIACUSzAy8ujuPPZdAq4C/izdsufNO75BvK1r/KtVmsgi2JeFKBABAgw0ImATmQTKBBIgbS0tEBmN2R5NTU1DVlZLIgCFAgfAU5dhU9fsaYUoAAFKEABCvRTgIFOP8HCNXldXZ3PqhsMBogfPihAAQpQgAKRJMBAJ5J600dbxI0RT5065TVFaWkpPv/8c6/v8w0KUIACFKBAOAow0AnHXhtAnVeuXInNmzd7PNMRAE2bNs3j+zxIAQpQgAIUCFcBBjrh2nP9rLcjiHEENc6niwBIBEJ8UIACFKAABSJNgIFOpPWoj/Z4GtVxBD6OQMjH6XyLAhSgAAUoEHYCDHTCrssGXmFHMOMIbkROHM0ZuCfPpAAFKECB4S/AfXSGfx8NqIbp6ekYNWpUr3OdR3UcAY8jAOqVmAcoQAEKUIACYS7AEZ0w70Bv1R87dqzHQMc5qOFojjc9HqcABShAgUgRYKATKT3Zj3Y4Lzx2Dnz6kQWTUoACFKAABcJCgFNXYdFNg6tke3s7PG2Pn5iYCOeNBBUKBbKzswdXGM+mAAUoQAEKDCMBBjrDqDOCVZVLly71yrq2trbXMbPZjOvXr3uc8uqVmAcoQAEKUIACYSDAQCcMOmmwVZw6dSrED4YEJcMAACAASURBVB8UoAAFKECBaBPgGp1o63G2lwIUoAAFKBBFAgx0IrSzxRQUHxSgAAUoQIFoF2CgE6GfgCNHjqChoSHArbPA3PIcMlRl0HVa+szbYtAiRyaDzP0nRwtD36f3mT8TUIACFKAABfoScAl0bF9M86A13OjrvJC971rHGzBo50Hm5xevrdL+ntMJw9FtKNvThnD9ThaLiwP3sMDc9jrWl72KRr8ytcDcfg6t2VXQd1lhtTr91Bci0eWT51eGTEQBClCAAhTot0CYf92MRGLhAViNG5EZG+CmdDajquBZtHT12zSgJ4hRmXvuuQc6nS6g+fYrM4sJLXvWYMlbKsybP8nPUy+jub4BmDoRcQHuGj8rwGQUoAAFKEAB8CtomH8IxKiM2APn4YcfDlHAcwOG3SuwQp+BZ5ffi9H+elku4cKZK0hWq6Do8xwLOnVlUMn+Dyrr6lBZkGyf7sqBZk8TTJ0GHK0sgEqaAktGwXOnYJKG2QZ6Xp8VYgIKUIACFIgQgT4CnZswtTh/8cggy9BAqzOgZ1KkEwadFpoMlf3LSYUMjRY6Q6cTkcin2ilNDjRaHQxmx6TQJeg0qVLeuxxfaH5NR3mahhJTTs+hQGVbG6IqqMSbWg0yZKnQ6Jz3k7mI00e2dKeTqQpQedTerk4dNElZ2GQyoaFoMmL8qotTc4PwtKOjI0QBzwiocp/D4Y0PQNnHp8Wl2WYj9K2jEPeP/XjU3heScV2LPUhxSW1/cRArtzdj0upTsFq/hvH4T9C06B6okjbg7H3Pot3ahasfrwA2/wprDn7iNKU40PM81YHHKEABClAgkgR8fHWJhafPY8HMQ4hZ0oAuaY3F1zCuvQXVWcvxYssVACJNFYoXnoL6hTbbOoyuP2NtzH5kLXvTvuD0Ji7WLUfKzGOIq2ix5XP1d1CfKEF6yUFcdMQ6QrXxDzg5diUM4kuusRhp/Z6OEmWVIb3gLGbovoLV2gXDqvE4vGZT73UlpqN4+/QkrDZ02b5Uaybh7Wx7u2IzUdF2HKVKJbKrPkZXMKbGBvgpGvqARw6F8p/9GJVxbZCl4wLOmFSYkPZLvGK0r88xrMKkPz2NBVuanAJl5/NSULp2OfISYwGMgDL1p0gTfVC+CiVpSsghhyLxHsxI/gJH/vT/nPIY6HnOZfM5BShAAQpEooCPDQMvo+nAq9Dnb0KR9CUjmj8CyvT5yM+uxv4PO7A8ZSSMH76PxuQHsVP6cgIgn4DMjfWwOrQ6T2Lb0jokl+vsX1YAFFNQuH0r9Eml2NZ4Hyoy7YmVM1Hw0J1QSF9odzhy8P+3VNYJ5O54C4uSxJcloEjKx/YaPY5muV2BpFyEtatnI1EhYj33do3xe05v48aNuHJFBH3BeRgMBo8Zi4BH/MyZMweTJ0/GW2+9BXEjz+HykCcWot5a6FodRSLuz7kLS7MqceAXe1GYONL1fb6iAAUoQAEKBFjAR6AzDpkVzTBCTE0dwrErYlXuF/jT9qexqRHIni9qMgKqH/4r0ot+j6qD/ws56EJ89n324EG8b0Fn8zFUm1TInzjONXhQqKBONmJN/V+xOvOuADTLUdZklE/5vlNZcijiE5AMt0DHY4nX0Ko3wowk2MIkj4lcDj7yyCO4du2ay7FAvhCLkQ8dOuQ1y9jYWPzqV78aVkGO18qKANbeF/p2M9Ar0JkEdXzfK3p65z/Q83rnxCMUoAAFKBBZAj4CHXE5cTWWZC7CXlM2SqsW454x/4ycF+qgLsnDGkdAkFKCw/ofoeHkW1hfZJ8iSi9F1doizMtMsGu1YFPWeGzyYKcM8zsTxMfHe2hV4A6dPXvWY2a333471q9fj7lz5/LeVB6FeJACFKAABSgAp4EPdw2LAQdKVuFobi3au+pRUfgQ8vJmIVN1DfpWk1NqsW4iHXmFFXjXakWXsRm1P+vAmqwFWN+9+HcuqvTXXfdSse+rYqzI9Hv0xKnQqH0qApw9e/agra0NYjRp1KhRw9DC0yJxUU373jrKbOSkDp9ptmEIyCpRgAIUoECABLwvRpaumgGSp93pcrWN5eoVOF+75F4PuTIFeY8VIF9pxJkLl6FIvR/5yo9x6uxnTlfJADA3oTIjATnaQG3IJ0esVNZ5SNMi3RWzf7l2vw7PJ+ER4DhsRyJx3gpsVjdgz5sf9SwaNn+EN/e8j9wdxUjv90JzR978TQEKUIACFPBfwHugE3sXcvJVaKjej0bTTSlHi+kUtpY9DW33gI79X+4ZZajrvpy8E4Zjx9CEPBTnTII8djoe3zEDR5Y+ha1NJluwY25D3fq1WIkl2Dgv0cewkv8NkVJKZd2L6vVb7PWxwGw4iA3rd6O7yv5mKa0husWW+poZ3VfC+3t+gNJNmTIFb775ZniM4Dhfwq9Iw/J9OzHr8mYkOm4BMbMaKNiJrXl3BK7PA+TMbChAAQpQIDIFfKzRGYf03/weu/9rLbJU35Zar3xkM7YV/B61cU9gqXRkJBIXbUXzmFexLf27mGOPJkS6HYeXYfaEEVKqCXkb0TjmTVRpUhDTKBJNwSOb16F538+RIl31FCjcEZDKGl2FDfb6KB/ZgleWPY4zjW/2rxD5JORq8lGdNRkxRWLqLTRXCSUmJkL8DI+HfSdqt4upAM/HpdG9FXuQt2JPH9WXIzZzI4zdl+rZk4vL/I1G13PlSSisN6K7CgM9zzVXvqIABShAgQgVkFnFTYgi/CHuj5Wbfg6atvLA3ypimNqdOXNGqtnUqWG+2nuY+kZqtcQNWNPS0sKyeWIH8Sj4cxaWfcNKUyCUAt6nrkJZq4GWLXY0ViWjQHu2e12INN224fe4uXz2ADYgHGhFQn+eCHAY5IS+H1gDClCAAhQIrUBkBTqx0/Gbw+uQfOLfMdq+LiQm5SV0zdqJfcvT+r27b2i7hqVTgAIUoAAFKDBYgaiYuhosEs+nQLQIiKmrcH5w6iqce491p0BwBCJrRCc4RmGf644dO+w3XLXd6FR8mXn7uXz5cti3lw0YuIAIFPz9EaX0J61zrVauXOnXuf0pg0GOszCfU4ACDgEGOg6JCP69dOlSly8VvV4vtdbTl81wul9WBHdJVDXt+vXrUnt//OMfw/Hj7R5uUQXDxlKAAkMi4OPy8iEpn4WEQODll1+WSm1sbIT4whk+l6+HAINFBl3g73//O0RQ7Xjce++90s1oHa/5mwIUoEAwBbhGJ5i6wzBvEdgsXLgQf/7zn1FbW4sPPvgAmzZ5ugvZMKw8qzSsBMT0pz/TRWI69NZbb5VGc0QDVCqV1I6DBw/22R5/y+gzIyagAAWiVoBTVxHa9adOnYJjLx3nJorRnCeffFI6lJubC8eojnMaPqdAIAUc06EiuBY/hw4d4ihiIIGZFwUo4FOAU1c+ecL3zc8++0yqvPNeOmI0RwQ269atk94TNwQVQY8IfjiqE759Pdxr3t7ejlmzZmH8+PFSVf/lX/4F/ozmDPd2sX4UoEB4CHBEJzz6KSC1dIzmON/xnKM6AaFlJj4Erl27Jr37ve99D+InPj5eGtnxcQrfogAFKBAwAY7oBIxyeGfkPprjqC1HdRwS/B0sAbHY3Wg0SlNWjjI2bNjgeMrfFKAABYIqwBGdoPIOn8w9jeY4asdRHYcEfwdDQFxeLtbmOC4tF2X87W9/C0ZRzJMCFKBALwFeddWLJDIO1NXVSQ3Jy8uTfs+ePRuvvfYaHNNW7lezNDQ0wGw2w5E+MhTYisEIiM9IuDz8uforXNrCelKAAoEV4NRVYD2HbW59Lf7Mzs4etnVnxUInEA4BRDgFZKHrSZZMgegV4NRV9PY9W04BClCAAhSIeAEGOhHfxWwgBShAAQpQIHoFGOhEb9+z5RSgAAUoQIGIF2CgE/FdzAZSgAIUoAAFoleAgU709j1bTgEKUIACFIh4AQY6Ed/FbCAFKEABClAgegUY6ERv37PlFKAABShAgYgXYKAT8V3suYHhsD+K55rzKAUoQAEKUMB/AQY6/lsxJQUoQAEKUIACYSbAQCfMOozVpQAFKEABClDAfwEGOv5bMSUFKEABClCAAmEmwEAnzDqM1aUABShAAQpQwH8B3tTTfyumpEDECvDGmBHbtWwYBaJegIFO1H8ECEABm8CaNWtcKMrLy11e8wUFKECBcBTg1FU49hrrTAEKUIACFKCAXwIMdPxiYiIKUIACFKAABcJRgIFOOPYa60wBClCAAhSggF8CDHT8YmIiClCAAhSgAAXCUYCBTjj2GutMAQpQgAIUoIBfAgx0/GJiIgpQgAIUoAAFwlGAgU449hrrTAEKUIACFKCAXwLcR8cvpvBLNGnSpPCrNGtMAQpQgAIUCLAAA50Agw6X7KZOnTpcqsJ6UIACFKAABUImwKmrkNGzYApQgAIUoAAFgi3AQCfYwpGcv6UN2pwE5GjbYAFgMWiRI0uFRnfJ71b7d44FZkM9Ksv2wSAK4oMCFKAABSjgpwADHT+hmKxvAXliIeqtzajIHNd34n6luIymqtVY2XKjX2cxMQUoQAEKUICBDj8DFIhyAYPBIAm0tbXhm2++iXINNp8CFIg0AQY6kdajIWxP72ko+5RTQTJkMhlkqgJUvrkLmgwVVBodOrvr+jU6Tv83Kh3pZMkoqKyHwSzmqS5Bp3kQWZtagIYiqGN8TI2ZDdBpNcgQZUk/OdBodfZ87IVZTGjZ45QmQwOtzgCzoy6dOmhUKuTsOoomp3Sqgudw1NBTY/hTFjph0Gml9nquj2hbKmQZGuyqLIBKMiqDrjOw83MikBE/dXV10k9paSnEj61OMmzevFlqvdncreDQ4G8KUIACYS/AQCfsu3D4NsBy8SBK0legdcZruGq1wmpYibGHt2FTo8mt0mex9+1zmLT6FKxWK7qMWzDh7SUofrEZZoxDZsU7OF6aAmRXQd/lbWrsClpeXI6FJ+7EC1e77PmsQEz1Y1h2wCCtIYLlE9QtzsZM3e2oMH4Nq7ULV1+4EycWzkFJ3Se2NFLNTGh4rBK1ox/FYVHvrnbUTHgH2cVVaJGCLz/KQifatE8gfeEJxFW0oEtq11OIO1EC9cyt9nzsDI1/wMmxK2Gwfg1jYzHSYv3/3/L69etSEHPmzBkpiNm7d68UxLgHMi+//DIcgcyCBQvwy1/+EteuXZOcdu3aJVUkNTUV3/oWL8R0+3DyJQUoEOYC/KsW5h04fKt/CY3bNuJI7jr8edEUKERFFVNQuH0r9EezUO1S8RSUrl2OvMRY6ahc+VMsyr8bz+w/C+PyNCT6871v6cCHR9uQPP8eJCpsJ8iVD2Dju+fsJVnQ2bgTS7WTUa4vQppyhHRckZSP7TV6JC3cicb7y5FpT60s1WB1XpKt3nIlUu9PgfKZ9/Gh8ddISeirLACdzXhlTRNyd7yFkjQlpBopp+GJ7VvRkbQQZQdycaTQvpZJORMFD90JBeRQJN5hr4Ht1+XLl3Hp0iUpKDl//rwUrJw9exZffvklRPAiHitXrpR+33vvvVAoFBCBzC233IJ169Zh1KhRtoz4XwpQgAJRKsBAJ0o7PujN7vwr6quNSC6/E0rnQEWhgjpZ6V/xrefQbrbAHv/4Pkcehx8+kISiNa/g4JQcwByP7MxEW6AinXkZzfUNMCmzMTHOFuTYMpRDEZ+AZNPvUd+8HJmpnoqxp0ED9O1mILGvsizobD6GatNklE/5vi3IcWQrtR+o1hul0SrHYU+/29vbcdttt/UKZMRojHg4RmI8nctjFKAABShgE2Cgw09ChAiMQcqKfdDffQwnaytQtKkBgBLppeVYW/QQMhPtzTQ9g6zvPuOhzSnwf4vFvsoagY4L5+A+QedcqOnMBXRY7nI+1Ot5fHy8NLXU6w0eoAAFKEABvwWc/63t90lMSIHhKRCLxMw8FFbUwyrWuzTvwM86nkNW+rM9C3yldT5WKYAQ64F6fryt/fHWUl9lfQtxExPga9xKOXUi4vh/nzdcHqcABSgQMAH+qQ0YJTNyEYi9Czn5KrRKUzRO75iN0Lf6GutwSjuopyOgTJmNxwpmQmk6hwsdCqTmZEPZehpnTTedcrbA3PIcMmTzoDUMdJ8e97K+QWzq/chXfoxTZz9zWuQMQGo/kKxWOU2rOVWHTylAAQpQIKACDHQCysnMegTGIf3xMuRWV2BDXZvt8m1zG+o2VGBTv+McBeLVjpuU3oDZ7GGvF/suzRmaup7Lyc0GHKtvAQr/DTkJtyA2vRg7ck9gadkuNEnBjrj8/SDWr3ge2LwC8xJH9lTf17M+yxoJxKbi0fI0HFn6FLY2mWzBjvkstMtKsEm9EhvnJbqu3fFVHt+jAAUoQIEBCzDQGTAdT+xLQD5hNrY2Lsf4Q3MxWuwRk/gMzmcuxuZsX5M6nnIdiYTcxVh1cw3UMZMw58A511EScYo8CYt278ey8YeQPjrGtkfM6Lk4NL4Yh8t/jgniky6/A3lba1Ez41NoVN+GTBaD0emHMH7Zfuxbnub/CIs/ZSEWSYXPobFmBjo0KYgR7R/9H9DP2Ar94RKk2K8M89RaHqMABShAgcAJyKxikQIfFBgqATEaklsEveZQEG4VMVSNiLxyxOaBa9ascWlYeXl5WCyGFnXnnzGXruMLClDASYAjOk4YfBpIAduuv6qCPWiTNtkTd/00oWnrM1hz8yHMSxsbyMKYFwUoQAEKUMCjAAMdjyw8OHiBcUj/zU7sSNYh0zGVFJON57tm4fC+JZy6GTwwc6AABShAAT8EuI+OH0hMMjABuTIFeSv2SD8Dy4FnUYACFKAABQYnwDU6g/Pj2RSICAGxzsXTIxzWvnCNjqee4zEKUMAhwBEdhwR/UyCKBTwFNN6CnyhmYtMpQIEwFOAanTDsNFaZAhSgAAUoQAH/BBjo+OfEVBSgAAUoQAEKhKEAA50w7DRWmQIUoAAFKEAB/wQY6PjnxFQUoAAFKEABCoShAAOdMOw0VpkCFKAABShAAf8EGOj458RUFKAABShAAQqEoQADnTDsNFaZAhSgAAUoQAH/BBjo+OfEVBSgAAUoQAEKhKEAA50w7DRWmQIUoAAFKEAB/wQY6PjnxFQUoAAFKEABCoShAAOdMOw0VpkCFKAABShAAf8EeK8r/5yYigJRKcD7XUVlt7PRFIgoAQY6EdWdbAwFAifg6UafzrkPxV3Dh6IM5zbxOQUoEHkCnLqKvD5liyhAAQpQgAIUsAsw0OFHgQIUoAAFKECBiBVgoBOxXcuGUYACFKAABSjAQIefAQpQgAIUoAAFIlaAgU7Edq33hl2/fh11dXVIS0vD5cuXvSfkO2EvYDAYpH4W/S36nQ8KUIAC0SbAQCeKetwR4MyYMQMffPABampqMHbs2CgSiL6mJiYmSv0s+lv0OwOe6PsMsMUUiHYBmbWva0ijXSgC2i8CnCNHjuDZZ59Feno6fvnLX0J8AfIRXQJidOfll19GY2MjnnzySeTm5mLUqFEDRhiKS7+HoowBA/BEClAgLAQY6IRFNw2skgxwBuYW6WcFKuAZiiBkKMqI9P5m+ygQ7QIMdCL0E3DmzBkUFhaiq6tLWqPxve99L0JbymYNVODLL79EU1MT/vGPf+DkyZP4wQ9+0K+shiIIGYoy+tVoJqYABcJOgDsjh12X+VdhtVqN/Px8LF++HLNmzcLPf/5zjBkzxr+TmSriBa5cuYK33noLYuZ69erVUKlUEd9mNpACFIhOAY7oRHi/i6uq9u3bh2XLlmH79u1YsGABFyBHeJ/7ap7j87B3795Br9MZitGWoSjDlxffowAFwl+AV12Ffx/6bIG4qmrp0qX44osvpHS33norduzYwcvKfapF3psiwBH9/uCDD0qjNydOnEBeXt6gFiNHnhJbRAEKRKIAA51I7FUPbfIW8HhIykMRJCAWpDPAiaAOZVMoQIF+C3Dqqt9kkXGC+Be+uMxYXG7OvXQio089tUL0c3NzM376058GfPRmKKaVhqIMT248RgEKRI4AR3Qipy/71RIR3Iipi7AJcixt0OaoIL74XH/mQWu44b3tFhNa9miQ0X1eDjTat9Biuun9nAh6R/RvdnZ2wIOcCCJiUyhAgQgXYKAT4R0cMc0zG6FvnY4q/XXpSiFxtZDt5wAKE0d6aeZNXDy4ATN3A4uajeiyWtFlfApxJ1Zh5n+dRKeXs3iYAhSgAAUiR4CBTuT0ZQS3xILO5mOoRgImxo3wv52W86jf+Q6S8x9FfooS4sMuV05DyeonkFx9DM2dFv/zYkoKUIACFAhLAQY6Ydlt0Vbpm+i4cA6m5ATEK/rxkZVGgcZg6sRxUpDjUJPHTcRUNKC+2e2Gpp06aFQq5FS+ifrKAqik6S4VMjTVaDFdguHocyhQ2abOVAXPoylKpr8cbvxNAQpQIBwF+vGtEY7NY50jQ8CMdv15KOP+jrpHk+1rdJJRUFnnc62NpeMCzpi8CRhx5sIl9B7TMaFh5S7oJq2CQZrq2oN/bdIgVZWBDWfT8Gy7FdarrSjHi5i95i1c7J2BtwJ5nAIUoAAFQiDAQCcE6CyynwKWS7hw5grUE36Cglda7WtzTmH1pGasWPA8Wsyeog0LzO3n0NrPokRyZakGq/OSoJCmun6E+9NUQPYTWF0yDUrxf4wiAdNnTIbpSDP0HsseQKE8hQIUoAAFgiLAQCcorMw0oALyJBTWn8O7Gx+wBRpS5rFIvP9+pOk3o+yAwcPITEBrwMwoQAEKUCBMBRjohGnHsdpiZEUFdTLQqjfC3AtEDkV8ApJ7He/rgBLJapU0mtNXSr5PAQpQwLPAFbRU/gaVLVc8vz3goxaYDfWoLNsHg6eBbEe+ZgOOVm7AHl9bbzjSDoff0vYhCcjRtvXjH60WmFueQ05RXZ9LCBjoDIdOZh2CIiAtOlZ6y1rVa5Gyt5Q8TgEKUMB/AQs6dZsw/+P78O8/CvSNlC+jqWo1Vrb42DsMFnQ27UbByg/R5X+lwzClHIqUfGjG7cRTBz/xGSAx0AnD7o22KlsMWuTIUqHRXXJtunRVlQr5OXch1vUd2ytpxOdKr0XHtkXKk6COF6tw+KAABSgQQAFzM15a/wnKNP8bE/gNG0BYT1mNQ3rRfLQv3YlGH9uFsBs82fHYsBKQJ+Zh4+Y4VO95G23di3870fbmq6jNLcPj6eM811c+CTnFD6J1zWbsbrNtD2gxncLWDc+htfRXeMjrRoOes+NRClCAAr4FbuJiw15sGZGF6QmOjUwvQadJhSzneeiaqqHJsO/wripA5VGD67S72QCd1mkn9wwNtDpHGpHPg8ja1AI0FEEd4+Eff2I0R7cGSVnPwIQ3UKQeBZVGZ98ctRMGnbanfJnYJV4HQ/ffVE8tE1NlOmg1OT070rvUyXaOxdSEPd1pxBWx9S75WkwtqOveskNs0eFP2TdhanHy8nKOPCELxbkNqHjT+1pNBjqe+pbHhpnAGKQs34XDsz7HM4kx9v/h5uIVPIw/bJ3d/a8m28iPzOl/7BGYkP04asrHoXryd6XzYlS/wpnkdTj8m+meR4GGWctZHQpQIIwEHJuUzv8JEty/XRs2YH3td1B0uB1W69cw1kzC29nL8aJjHY/5LLRL5mDhidtRYfzalqbidpxYmI6ZlU0wYxwyK97B8dIUILsK+q5mVGS6/yNPjtjMcrQdXwUl5ko7yRsrMhGLTrRpn0D6whOIq2hx2iW+BOqZW71cuQrA3IwXi0txQv07XJV2o/8axrW3oDprDQ7Y1/9YLtZhccps7EYx9Fe7YL36Gma0rkB6yUHb2hlzE7YsKMahmMfQ0mXb0b7LuAIx1Y+h+MVm10Cvu6tv4mLdcqTMPNZdX+vV30F9oqQnX0da+fcxZdokNOz/vzjnbd2SlQ8KUIACAxAAxJX+wX0MRRnBbQFzjyqBr45bS5Up1tLjnzs1+3Pr8dIUK5SrrMe/6uo5LqVVWrOrPrZ2WbusXx1fZVUql1hr27/uSeM4jrnWKv11q9Vqzyu7yqp3ysrpBKu11zlWq1Uqa4q1sPaC1eU0lzq45iJedemrrNndZfd+32q9btVXzXVrm70t0nn/Y2+XW9sd5zna0fWxtSr7B3YLR30dNk7levR1Lk8Y9X64x5yOGIm/KUABClCAAhToh0C/1v+5XDV6Gc31DTAl340pSufb3DiuHj0PfXvva0v9q5r9FjqmyZg25fsuu8T7vnIVkKum4IH0k1hT9RaadG9BZ3C7Q6DlAk7uPwm47FovRpU2wmgV9yG8xfbcWI60jvdQV1eHuro3odXMgrroDS/Vd9TXwwUjkpkR1fV/dbpXYd9GDHS8UPMwBShAAQpQwH+BgW9SCmlTVKOPorzt5O7jlO637LfQ6X7d+4npzAV0eJr2UaRhxeFG1NzzJWrXP4YstVgC4M/6GqcyxJRcwQ8xWr0A2//0hdiGFWNyNqG5ai7Qeg7tXtcItWBT1vietUHiljwxk1HU4HW7e6dCXZ8y0HH14CsKUIACFKDAAAQcIwsDOXUcJk5V+TjRw+iGj9Sub41A3MQEeN1pQ+wGP3Ui4rxFA4pEZOYtRsW7Rli7jGiufQAda7KQvr7RaVTFtcSeVzdgOPBbFB2dgdr2C3i3YjHy8vKQlzkBX+nP9yTz+My2xsgqrQ2yre1xPLetO/J4kseD3prmMTEPUoACFKAABSjgWcC2d9dAppnGIjUnG8rW0zjrcrNgxyjRYLbDkCM29X7kKz/GqbOfue43I23RAf83SZUrkZK3CAX5KZBGgTAR0+dP7zUyY7swRIUc7Z/wiQho3KfkLP+DK5e+9owIX/VtQmWG+8aCfRsx0PFCzcMUoAAFKECBfgl42bur7zzkiE1bgPIHTmBp2S40ScGOBea2aixbuBvqzSswT9oOQ4F49SR7djdgNn/jIWvnkSULrpmvwRKbikfL03Bk6VPY2mSyBTtiSmlZCTapV2LjvETXtTv2XG0BSw40dW32q6PE5ebvob4JKCzO2TZElgAAAh9JREFUQoJ8JBJyF2OV+gDWP3scJjH9ZbmIxt370ZAu8p2Ge0QA17Afuxsv2sq1mNC09Sks1Z71UHf7odjpeHzHDLf6tqFu/VqsxBK3+tqn5rIfdLqk3zVrBjquHnxFAQpQgAIUGJiAPBEPaeah1delzt5yVkxB4fO1qJnxKTSqb0Mmi8HoX3+EGTWNOLwizX5bGntgcXMN1DGTMOfAOdcRGnve8oQcaFZ9hSL1d/CdOa/jnCUWSYXPobFmBjo0KYgR611G/wf0M7ZCf7gEKQrPoYA8cSF2Nxdj/KG5GC3OEXVKP4Txy3aifPYdUnAkVz6A8n37sKirEqoYsY7mx1jftRDN+5YgRfEtxKYvw+HdU/F+Vryt3Pgn8d5tBThYW+pjOm0EJuRtdKvvXBwaX2zP16m+0oLo08j2dEm/3UMmLsTy5s7jFKAABShAAQr0Q8DchMqZzwCVr2BFSqBvAdGPekRJUjHqlJt+Dpq2cmTGOgVATu33fNQpAZ9SgAIUoAAFKOCngCIVj62djBd/r+vzZpN+5shkXgUuobFqP+J3FCPdS5AjTmWg4xWQb1CAAhSgAAX6KyBHbPoSvPR9HV77S6DvXt7fukRyenH38mpUXCrGb+3TaN5ay6krbzI8TgEKUIACFKBA2AtwRCfsu5ANoAAFKEABClDAmwADHW8yPE4BClCAAhSgQNgLMNAJ+y5kAyhAAQpQgAIU8Cbw/wF7gkZqy4ilNQAAAABJRU5ErkJggg=="></p>
<p>Light from a laser is incident on a double slit. The light from the slits is detected by a&nbsp;light sensor attached to the train.</p>
<p>The graph shows the variation with time of the output voltage from the light sensor as&nbsp;the train moves parallel to the slits. The output voltage is proportional to the intensity of&nbsp;light incident on the sensor.</p>
<p style="text-align: center;"><img 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"></p>
<p>&nbsp;</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain, with reference to the light passing through the slits, why a series of voltage peaks occurs.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The slits are separated by 1.5 mm and the laser light has a wavelength&nbsp;of 6.3 x&nbsp;10<sup>–7</sup> m. The slits are 5.0 m from the train track. Calculate the separation&nbsp;between two adjacent positions of the train when the output voltage is at a maximum.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the speed of the train.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the width of one of the slits.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Suggest the variation in the output voltage from the light sensor that will be observed as the train moves beyond the first diffraction minimum.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In another experiment the student replaces the light sensor with a sound sensor. The train travels away from a loudspeaker that is emitting sound waves of constant amplitude and frequency towards a reflecting barrier.</p>
<p><img 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"></p>
<p>The graph shows the variation with time of the output voltage from the sounds sensor.</p>
<p><img src="data:image/png;base64,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"></p>
<p>Explain how this effect arises.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«light» superposes/interferes</p>
<p>pattern consists of «intensity» maxima and minima<br><em><strong>OR</strong></em><br>consisting of constructive and destructive «interference»</p>
<p>voltage peaks correspond to interference maxima</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s = \frac{{\lambda D}}{d} = \frac{{6.3 \times {{10}^{ - 7}} \times 5.0}}{{1.5 \times {{10}^{ - 3}}}} = ">
  <mi>s</mi>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mi>λ</mi>
      <mi>D</mi>
    </mrow>
    <mi>d</mi>
  </mfrac>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>6.3</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>7</mn>
          </mrow>
        </msup>
      </mrow>
      <mo>×</mo>
      <mn>5.0</mn>
    </mrow>
    <mrow>
      <mn>1.5</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>3</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
  <mo>=</mo>
</math></span>» 2.1 x 10<sup>–3&nbsp;</sup>«m»&nbsp;</p>
<p>&nbsp;</p>
<p><em>If no unit assume m.</em><br><em>Correct answer only.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct read-off from graph of 25 m s</p>
<p><em>v</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{x}{t} = \frac{{2.1 \times {{10}^{ - 3}}}}{{25 \times {{10}^{ - 3}}}} = ">
  <mfrac>
    <mi>x</mi>
    <mi>t</mi>
  </mfrac>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>2.1</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>3</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mn>25</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>3</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
  <mo>=</mo>
</math></span>» 8.4 x 10<sup>–2</sup> «m s<sup>–1</sup>»</p>
<p>&nbsp;</p>
<p><em>Allow ECF from (b)(i)</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>angular width of diffraction minimum =&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.13}}{{5.0}}">
  <mfrac>
    <mrow>
      <mn>0.13</mn>
    </mrow>
    <mrow>
      <mn>5.0</mn>
    </mrow>
  </mfrac>
</math></span> «= 0.026 rad»</p>
<p>slit width =&nbsp;«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\lambda }{d} = \frac{{6.3 \times {{10}^{ - 7}}}}{{0.026}} = ">
  <mfrac>
    <mi>λ</mi>
    <mi>d</mi>
  </mfrac>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>6.3</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>7</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mn>0.026</mn>
    </mrow>
  </mfrac>
  <mo>=</mo>
</math></span>» 2.4 x 10<sup>–5</sup> «m»</p>
<p>&nbsp;</p>
<p><em>Award <strong>[1 max]</strong> for solution using 1.22 factor.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«beyond the first diffraction minimum» average voltage is smaller<br><br>«voltage minimum» spacing is «approximately» same<br><em><strong>OR</strong></em><br>rate of variation of voltage is unchanged</p>
<p> </p>
<p><em>OWTTE</em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«reflection at barrier» leads to two waves travelling in opposite directions </p>
<p>mention of formation of standing wave</p>
<p>maximum corresponds to antinode/maximum displacement «of air molecules»<br><em><strong>OR</strong></em><br>complete cancellation at node position</p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>On a guitar, the strings played vibrate between two fixed points. The frequency of vibration&nbsp;is modified by changing the string length using a finger. The different strings have different&nbsp;wave speeds. When a string is plucked, a standing wave forms between the bridge and the finger.</p>
<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>The string is displaced 0.4 cm at point P to sound the guitar. Point P on the string&nbsp;vibrates with simple harmonic motion (shm) in its first harmonic with a frequency of&nbsp;195 Hz. The sounding length of the string is 62 cm.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline how a standing wave is produced on the string.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the speed of the wave on the string is about 240 m s<sup>−1</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch a graph to show how the acceleration of point P varies with its displacement from the rest position.</p>
<p>                 <img src="data:image/png;base64,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"></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, in m s<sup>−1</sup>, the maximum velocity of vibration of point P when it is&nbsp;vibrating with a frequency of 195 Hz.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, in terms of <em>g</em>, the maximum acceleration of P.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the displacement needed to double the energy of the string.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.v.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The string is made to vibrate in its third harmonic. State the distance between&nbsp;consecutive nodes.&nbsp;</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«travelling» wave moves along the length of the string and reflects «at fixed end» <strong>✓</strong></p>
<p>superposition/interference of incident and reflected waves <strong>✓</strong></p>
<p>the superposition of the reflections is reinforced only for certain wavelengths <strong>✓</strong> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mn>2</mn><mi>l</mi><mo>=</mo><mn>2</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>62</mn><mo>=</mo><mo>«</mo><mn>1</mn><mo>.</mo><mn>24</mn><mo>&nbsp;</mo><mtext>m</mtext><mo>»</mo></math>&nbsp;✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>f</mi><mi>λ</mi><mo>=</mo><mn>195</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>24</mn><mo>=</mo><mn>242</mn><mo>&nbsp;</mo><mo>«</mo><msup><mtext>m&nbsp;s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> ✓</p>
<p><em>Answer must be to 3 or more sf or working shown for<strong> MP2.</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>straight line through origin with negative gradient <strong>✓</strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>max velocity occurs at x = 0&nbsp;<strong>✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mo>«</mo><mo>(</mo><mn>2</mn><mi>π</mi><mo>)</mo><mo>(</mo><mn>195</mn><mo>)</mo><msqrt><mn>0</mn><mo>.</mo><msup><mn>004</mn><mn>2</mn></msup></msqrt><mo>»</mo><mo>=</mo><mn>4</mn><mo>.</mo><mn>9</mn><mo>&nbsp;</mo><mo>«</mo><msup><mtext>m&nbsp;s</mtext><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>»</mo></math>&nbsp;<strong>✓</strong></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msup><mfenced><mrow><msub><mn>2</mn><mi mathvariant="normal">π</mi></msub><mo>&nbsp;</mo><mn>195</mn></mrow></mfenced><mn>2</mn></msup><mo>×</mo><mn>0</mn><mo>.</mo><mn>004</mn><mo>=</mo><mn>6005</mn><mo>&nbsp;</mo><mo>«</mo><msup><mtext>m s</mtext><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>»</mo></math> <strong>✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>600</mn><mo> </mo><mtext>g</mtext></math>&nbsp;<strong>✓</strong></p>
<div class="question_part_label">b.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>∝</mo><msup><mi>A</mi><mn>2</mn></msup><mtext mathvariant="bold-italic">&nbsp;OR&nbsp;&nbsp;</mtext><msup><msub><mi>x</mi><mtext>o</mtext></msub><mn>2</mn></msup></math>&nbsp;<strong>✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>4</mn><msqrt><mn>2</mn></msqrt><mo>=</mo><mn>0</mn><mo>.</mo><mn>57</mn><mo>&nbsp;</mo><mo>«</mo><mtext>cm</mtext><mo>»</mo><mo>&nbsp;</mo><mo>≅</mo><mo>&nbsp;</mo><mn>0</mn><mo>.</mo><mn>6</mn><mo>&nbsp;</mo><mo>«</mo><mtext>cm</mtext><mo>»</mo></math>&nbsp;<strong>✓</strong></p>
<div class="question_part_label">b.v.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>62</mn><mn>3</mn></mfrac><mo>=</mo><mn>21</mn><mo>&nbsp;</mo><mo>«</mo><mtext>cm</mtext><mo>»</mo></math>&nbsp;<strong>✓</strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.v.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A loudspeaker emits sound towards the open end of a pipe. The other end is closed.&nbsp;A standing wave is formed in the pipe. The diagram represents the displacement of&nbsp;molecules of air in the pipe at an instant of time.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAxIAAAEACAYAAAAnRUByAAAgAElEQVR4Ae3dC1yUdd7//3fc+3CLH7GtuWlahgGxnl02S8NVKtPMe8VDd92pFeapzDzklt0JoWEWlnkqt241wajWNhE6uXlIdEUtjTIrlwaSLA13zS12/tR6Pxr+j+8Fg8M4g4AwzOF1PR7IzDXX9T08vyPMh+/pnMrKykpxIIAAAggggAACCCCAAAINEAhrwLVcigACCCCAAAIIIIAAAghYAj8z/8ZEdYIDAQQQQAABBBBAAAEEEKhToLj0UM3r5ziHNplgwvWFmit4gAACCCCAAAIIIIAAAiEt4ClWYGhTSL8lqDwCCCCAAAIIIIAAAo0TIJBonBt3IYAAAggggAACCCAQ0gIEEiHd/FQeAQQQQAABBBBAAIHGCRBINM6NuxBAAAEEEEAAAQQQCGkBAomQbn4qjwACCCCAAAIIIIBA4wQIJBrnxl0IIIAAAggggAACCIS0AIFESDc/lUcAAQQQQAABBBBAoHECBBKNc+MuBBBAAAEEEEAAAQRCWoBAIqSbn8ojgAACCCCAAAIIINA4AQKJxrlxFwIIIIAAAggggAACIS1AIBHSzU/lEUAAAQQQQAABBBBonACBROPcuAsBBBBAAAEEEEAAgZAWIJAI6ean8ggggAACCCCAAAIINE6AQKJxbtyFAAIIIIAAAggggEBICxBIhHTzU3kEEEAAAQQQQAABBBonQCDRODfuQgABBBBAAAEEEEAgpAUIJEK6+ak8AggggAACCCCAAAKNEyCQaJwbdyGAAAIIIIAAAgggENICBBIh3fxUHgEEEEAAAQQQQACBxgkQSDTOjbsQQAABBBBAAAEEEAhpgSALJBwqz09Tj6ixyrL9KOlH2TLHKqZLmvLLHU3X0I4iZSXFa0RmkZow1aYrX3OnZLfp3cUZyraMmzsz0kcAAQQQQAABBBDwR4EgCyTcic9VbHK2ij+bp8TIIK+qe9Wb7blD5fuyNWPpAf3UbHmQMAIIIIAAAggggIC/C/Dp2t9biPIhgAACCCCAAAIIIOCHAoEdSDjKVJi7WJO6dFJMVCf1mLBUmz486sLsPrTJIbstX1kpSdb15p6YISnKyrfJbt11amjUmvytWj6hb/V1SUp9ca/K6hjH5CgrVN7iieph0rS+kpSamS+b3fWmkyorfFmpQ7pWXdNlopZsdeZdVWxH2V5l15Svq4amZCrfVl5dJ2f5btOS3FwtcS9fuRly5CxDX01atrt2mY3Xiyka6ixjrbpLKs9XapeuGvHCVu1zua7HhOV61yqDyX+e+iWvVYUKlH5DZ/VIyZezdC7wPEQAAQQQQAABBBAIcoEADiS+U+HSe3XL899paN5+FZeWaNfsTtq/aZcqvDWa/QOtmpamgpgF+qj0kIpLi7Rz9nl6NXme1tca71+gx6b8SZq8QZ+XluijzeOklydr/NK91QGHWwb2vVo2bqbe+o+7tOkLk+4hfb5nmv5j3f2asfKD6ntO6mjubA0auU6anKOPTLobBuiz++7Qg7mHrbkWjqO5mnrdNO246CHttNLZradj3tO0pDTlHT3pkukePfP8h+o0+52qOmRepcLUW9Svz0J92i+9Ku137pWeu1+Pvl6VthyHlXfvCCVvv0Tz9hRZXh8t+bUKppzKvyqDCh14dJnyzr9d64zRFwVa1mGLJk3LUqFdikxM087MOxSuBKVuPqiP5ycq0qVkPEQAAQQQQAABBBAIDYHADSTKP9KGlcd12+z7lBRrPsqGKSJ2mB6YfbPCvbSd45tPtf3gpUpIiFaEdU0rtUuco7dKs3Vn7Lkud7XToAWpurd3O4XVpPt7fbXyTe07bdK2mTPwpl74MlGjk69Wu2rRsHYJGnNrFxXlf6pvTKeE45A2r9kkjZ2pB4bHKcKkG3ejRo9spU1r3lWJ47h2rFisTbGT9cDUvtXpRCouOV3LRhYqdcUul7/8d3Spdyu1i09QfHi4uj/4B5cy91ZCbLl27vtCdjlUvmO1UjdGa9bsZF3ZrlWVV9xoPbVikHY+vFo7XOoVXlNGc1k7xV/bS+EH39OBb1yDGRcuHiKAAAIIIIAAAgiEnECABhIOlRduU17FpYrpUBUSVLVcmCI6dFK0l2YMu7irBnT+UIuy3ta+/Lddhgy53xCtq7tepFM41elW5Gtr4Qm3i8MUmThPH3+WpiuP7VRebq7ycnOUlXKrhswtqLnWUbJbuful6JiLq4MY81IbJc7fruK8ZMXaP9HWnMMK7x6ltqcylhShDjGXqiJnmwpdPuzXJFyvBydUuCVfFeHRuqytCSKcR131crtGX6n4SNUAMOcrfEcAAQQQQAABBBAIXYGfBWbVT+pYaYn3IUzeKhXRWzP+nKteW/6qvIxFeuWgGQTVQ7fNnak7bu6vWNeYxGMax/VJ6bdy9Hd70f6psmZMUPqWcsWNnaVJV7bWBQPT9WrMQt2y8JCO2B1egxu3lFSRPU7x2e5nJYW7hkfuAZSH6z2dqlirCT3Wenilo7p5OMspBBBAAAEEEEAAAQS8CQRoINFKbaOiFa4Sb/Xyfj4iVonDzdddSjeTj19/Rc89PE6jitdo53z3CME9mTbqFnWhwvStyws/yvba40rf1UeLdmUoqb3zL/7HlZ/ylVTvEMIkGa7uc3O0PjnOpTfEJSszRMn1aUMf90zTxg3Jiq3V4+GSyFkl7pIODxFAAAEEEEAAAQSCXsDbR0o/r3iYIuOvVVK4+3Abh+xHDtU/vDDj/4ffrtEjO6riQKmO1Syw5CXd8ERdH9/azcauI8VfSbE91cWae1D9sqNC3397ak5BWHRfDe8plRR/4zJhu3pVKbOB3rEYXT+yjUreO1h7pSV9p8LFoxSTlClbTfncinDGp60VPzBR4bb9+qzsVJkkh+yFyzW0ZgO/MybEBQgggAACCCCAAAIIWAIBGkhIirxG9yyIV96UVGUVmT+lm6VdX9eTGa95HfLksGVqRFSSUnOLapZ7tdt2ausH0qBx1ym6RuOwXslYrrzqJU/tRS/rD1M2qd+C8ep/2sZ21R/S92/QSzuOVu107SjTvmfSlbqx7NTbLKyTBs8crUuzF+vp/KrrHGUFemndZ4qbPl2jYi9R/ykz1W97huY+41y2tVy23MVKXSpNTRvuvSfhVC5eHoUpsv94pQ/Yo9RHXtA+K5io8sqYs0ay8nedbO4lGeu06zwUhyrsFaG5u3ddRLyGAAIIIIAAAgiEgEDNR+fAq2srtR8+T+uXd1HBiJ6KiYpWr2kfKn7yOHX3Upmw2NH6Y844XfhmsnpZeylEq1fSW7pw8mI9Mqyjy3CiHrrt1jgdyhhcle6I7eqyfK0WDne9xpmJ+ZB+jzLTu2tvcoKuMOl2S9XOS8bohSVjXFaQMitEPaDVObfqp4wbrOuu6LNMP41+Xqun97YmYIe1H6aFeY8r4e9PqN/lZj+Knhr15gWalPOspsVf4Mywcd/DOirpybVa1u9rpfWJq6qXVfdVNfnXN+Gw6EGafue/lH5DV/UY86pKGt1TUt8cuQ4BBBBAAAEEEEDA3wTOqaysrDSFMpuomf0PQvtwbrhWolmbV7ktCRvaMtQeAQQQQAABBBBAIHQFPMUKAdwjEboNSc0RQAABBBBAAAEEEGhpAQKJlm4B8kcAAQQQQAABBBBAIAAFAnT51+aSrt5crrS50iddBBBAAAEEEEAAAQSCQ4AeieBoR2qBAAIIIIAAAggggIBPBQgkfMpNZggggAACCCCAAAIIBIcAgURwtCO1QAABBBBAAAEEEEDApwIEEj7lJjMEEEAgmAV+lC1zrGK6pCm/nA1mgrmlqRsCCCBgBEIgkCiXbeuzmvtiURPswOyeVgv80nQUKSupq3qk5Mvs512/o77ldK9f/VLnKgQQQKBK4FzFJmer+LN5SowMgV8vNDsCCCAQ4gLB/5O+vFBr71uh/T81QUs3ZVqNLU5YnO7M+1Qfz09UZGPT8HafP9TPW9k4jwACCCCAAAIIIOBXAsEfSPgVN4VBAAEEAlSgPF+pXbpqxAtb9f6yieoR1UkxUV01NOVlFZadrK6UW+9nve6putVRtlfZKUkyO6dWpZupfFv9+10DVJViI4AAAgEtENyBhPkl1mecXqmo0IG5N+qKmnG7Dtlt+cpqyC8tr2mZ9j+qj95ZqkldzC/ATorpMlFLttpkd31rOMpU+GKKhlq/JDspZkiKsvLdrnG9Xg6V56epR1SSUl94qjrtAUrd+lcPQ5vMkKTlNfn3mLBYGzJNXgOUmn/cJdU6ylln/VyS4CECCISwQIUOPJqiVbpLm744pOJPcjRJ63TLuOdVaPc2J+LM9ziO5mrqddO046KHtNOkW7pbT8e8p2lJaco76gxSQpidqiOAAAJ+KhDcgURkotL3rNFt4eHqPvcv+twatyvZi17W/Un/owLnL60vtmreRQWadsM4LSn8znNTeUyrmq9ilzbv76QH3i9RcWmRdq6I0ubxD2mVMy3HYeXdO0LJ2y/RvD1FKi4t0UdLfq2CKXfowdzDZ5i78bHydrXTrPdL9PmeNRrXu41b+U7qaG6aRt33mRI27LfS3vXAr7Rx4UsqcrtSdZWzrvq5p8NzBBAIWYHwIbM1d2pftTM//iLilPTgTN325WvasO+EV5O67zmuHSsWa1PsZD3gTFeRiktO17KRhUpdsasB88G8FoEXEEAAAQSaQSC4AwmPYCe078WV2jPA5ZdhWDtdOe1xLRt7XM/My5XN2x/WPKYnKfxmPfDgMMVGGM5Watf/Zt3S85C2f3xMDtOzsGO1UjdGa9bsZF3ZrpU1xz0ibrSeWjFIOx9erR11rm7SUUljb1RcRJjC2l2uy608XApSvkt/fHiP+i34H90eZ2ZNhKkq7TsU7nKZ9bDOcrpfzHMEEEDAXSBc0Vd3rgoinC9FXKyY2OPK2/KJlw/8Z7in/BNtzTms8O5RalvrN1KEOsRcqoqcbSqs82eksyB8RwABBBDwtUCtH9u+zrxF8rN+aR0//Zehqn5pyXZIR7x20TekxP9WSfE3suuECrfkqyI8Wpe1NUGE8whTRIdOiq7I19ZC73/Jc17t+btD5YXblFcRrau7XuSyBFd12p5vcjvrLKfbaZ4igAACDRCoOFCqYw38I4zrPRXZ4xTvHPppfe+sIXMLGlACLkUAAQQQ8LXAz3ydYUvn5zhWqk8q6ihFRYm+PHZSijy3josa8VLFWk3osdbDjR3VzcNZTiGAAAKBJODsUTjWgEI775HM8NMcrU+Oc/mDSAMS4lIEEEAAgRYRCLkeibC2Uep22pgfF/vTeg5cXjubhz3TtNGaRGgmErp+bVd6ovu8h7PJiHsRQACB5hKoqO5pdUnf/o2KbW2UNLCblyWpz3BPZDddP7KNSt47qLJaPRrfqXDxKMUkZTZ8uKlL8XiIAAIIINB8AiEXSMjrLy27jhR/JcV2Ugf3eQhn5d9a8QMTFW7br89qlkg0CTpkL1yuoVFjlWX7sZE5hCky/lolhX+l4iOua0Q5ZD9ySCWNTJXbEEAAAW8CFdmL9WRuUdWqdPZPlXX//yhvwEzd09/7H0TqvqeN+k+ZqX7bMzT3md3VwUS5bLmLlbpUmpo2XLGh95vKGz/nEUAAAb8SCP4fz9ZEwJ9XoVfYZXe01pW3T1Qft19aRZmpmpbdpu5fWqelVZ+2DFNk//FKH7BHqY+8oH1WMGGWn31dGXPWSNOna1TsWQyjirxG9yyIV17GcuVZa65Xpf1kxmuqawSXx5I3qn4eU+IkAggEpUC44sYmKf7QU7rGzGPoNkEFXR/V+ieHqb3X3yZnvies/TAtzHtcCX9/Qv0uN8to99SoNy/QpJxnNS3+gqCUpFIIIIBAMAgE/xyJsE4aPHOUXk2+UVfMTVDq5lW6M260ns67ROuzzC+tj82yS4ob+4CWbR6pxNg69os+La1ndE193gVhHZX05Fr94rUspfWJq1qWNXygpi5YpdXD4hVRnzS8XtNK7YfP0/rzs/RkUk/NqpDCB96vRZPH6ZMZb3i9y+MLp9Vvle48myDHYyacRACBQBZoFZOgpOS7NGKmp1qcq9jkbBUnV79WvZ9c3feYa8MUEZuoO+ebL0/pcg4BBBBAwB8FzqmsrKw0BTMbqZmx+xzBIeCwZWpU0iFN35OmxEivfyoMjspSCwQQaH4Ba9PKe/XJgw2YFN2Ye5q/JuSAAAIIINAIAU+xAp8wGwHpV7eYX9Rd+mpS5qc1O2k7ynbr2Yw1OjnxP3UlQYRfNReFQQABBBBAAAEEgkWAHomAb8mTKit8W39akaFntpRV1cYaNnWP/ntYfO2NowK+rlQAAQQQQAABBBBAoCUEPPVIEEi0REuQJwIIIIAAAggggAACASTgKZBgaFMLNuCRI0f0ww8/tGAJyBoBBBBAAAEEEEAAgcYJBP+qTY1zafa7Tpw4oQEJ/bRoyWIlDR9er/xMJMiBAAIIIFAlwAIhvBMQQACBlhUgkGgh/1fXvWrlvHTJEg0aPFjnnXdevUrCL856MXERAggggAACCCCAQDMLMLSpmYE9JW96I57KyLBeuiYhQZveecfTZZxDAAEEEEAAAQQQQMBvBQgkWqBpTG/EH2bPtnK+MzlZpleCuRIt0BBkiQACCCCAAAIIINBoAQKJRtM17kZnb8Qtt95iJRAbGyt6JRpnyV0IIIAAAggggAACLSdAIOFje2dvROvWrWtypleihoIHCCCAAAIIIIAAAgEiQCDhw4Zy741wZk2vhFOC7wgggAACCCCAAAKBIkAg4cOW8tQb4cyeXgmnBN8RQAABBBBAAAEEAkGAQMKHrWRWanLOjXDP1tkrUVBQ4P4SzxFAAAEEEEAAAQQQ8DsB9pHwYZNsL9gp17kR7lnPSUlxP8VzBBBAAAEEEEAAAQT8UoBAwofN0qFDhzpzq++mdHUmwosIIIAAAggggAACCPhAgKFNPkAmCwQQQAABBBBAAAEEgk2AQCLYWpT6IIAAAggggAACCCDgAwECCR8gkwUCCCCAAAIIIIAAAsEmQCARbC1KfRBAAAEEEEAAAQQQ8IEAgYQPkMkCAQQQQAABBBBAAIFgE2DVpmBrUerjcwGbzXZanv/+8d/SOdLPf/7zWq+Fh4frTKt31bqBJwgggAACCCCAgJ8KEEj4acNQrJYXOHHihL799lt9+eWX+v/sdn3++ef6/vvvVVJcrL3vvV9TwME3DdEvf/nLmufmwT/+8Q/r+a9+9ata5//5z3/qnbc31pxz3vuLX/xCV1xxhf5fRIQuu+wyXXjhhXXuOVKTAA8QQAABBBBAAIEWEiCQaCF4svUfgR9++EFff/21Pvv0UytYKC0ttT7sd4y6TNckJOiSSy7VxRe3U7/f/U5t2rRRU/YqOHszjh8/rr8fO6ZiW7Hyt23TroICHS79Uv89ZrSVf0xsjBVgmB3QORBAAAEEEEAAAX8QIJDwh1agDD4VOHLkiA4ePGh9aN+ev83qXTAf2Dt37qzfxMdr+IgRenbFCp+UyRkYOL+7Z2oCDdMjcqyszAow/vTSyzK9GN2791DPXj0VFxdHz4U7Gs8RQAABBBBAwCcC51RWVlaanGKiOqm49JBPMiWTKoGGmjf0epyrBMwQpaKiIu3861+18e23rZNDbrrJChrMMCJvH+L91c8ZXHxYWGjVp23bthqQeK0VWPTq1UvskO6vLUe5EEAAAQQQCFwBT59DCSRasD09NUhdxWno9XWlFeyvmV4Ha4jQrl3WMKXJU+6xAgfT6xBsk52dPSwmsHh+xR+tHotBgwbpyt69g66uwf6+pX4IIIAAAgj4q4Cnz6EEEi3YWp4apK7iNPT6utIKxtf279+v3bt2ywxXMsd//v736ta9u3r27BmM1fVaJ+PwyYEDevONN2ocEq+9lqDCqxgvIIAAAggggMCZBDx9DiWQOJNaM77uqUHqyq6h19eVVrC85ux5WL1qlcwQHxM88KH5VOs6fQgqTpnwCAEEEEAAAQQaLuDpcyiTrRvuyB0tLGDmPBQWFmr1ypU6duyYxk+YoBdfeom/uHtoFzOMa8zYsdaXM6i4fcwYde7SRSNGjlRCQgJzKjy4cQoBBBBAAAEEzizAztZnNuIKPxEwQ3aeXLhQV8X/VmY+wEMPP6x38/OtD8nBNu+hOcidQYUxmzR5smXYvXMXPffH5+RchrY58iVNBBBAAAEEEAhOAXokgrNdg6ZWZo+HgoICq/fBVGr8xIk6cPAz/op+li1s5o2Yr6n33Wf5PpKSYqVofOmlOEtcbkcAAQQQQCBEBOiRCJGGDrRqmuFL5i/l5i/mzt6HV9at08CBAwkimrAxzVKxxtTYmh4eYz10yBDL3rQBBwIIIIAAAggg4E2AHglvMpxvEQEzxCYrM9Pa2fmWW/9b7xd+wIZrPmoJZy+FmXPy6rpXdfPIkTL7bZgN+gJtrw0fkZENAggggAACIS1Aj0RIN7//VN7Mf0iZM0eTJ05U79699dbGjbr7nrsJIlqgiVq3bm3Zmza44oorrDYxbWPaiAMBBBAIFAGzwgw9q4HSWpQzUAXokQjUlguScu/evVvLliyxajNtxgzNf+yxIKlZ4FfDDHtKGj7c+jLt9MSCBTXt1Ldv38CvIDVAAIGgFzA9qw+npFhDOBtSWROEhPJRXHoolKtP3RsgQCDRACwubToB9wCCD6ZNZ9scKZn2MV/OdjPBnwn8aLfm0CZNBBBoKgGzNPiCxx7ThpwcPTxnToOWCQ/VD9OhHkQ11XsvVNJhaFOotLSf1NMMj7nt1lutXgjzQdRM8uXDqJ80Tj2KYdrKtJlpOxNMmLZkyFM94LgEAQRaRMAse/3sihUaNGiQBiT0U15ursxqgBwIINA0AvRINI0jqZxBwDmJuqS4mL9kn8EqEF42AYX5cg55io6J0Z3JyUzKDoTGo4wIhKCAGab5u/799fSiRfrTK6/o0fnz+XkVgu8Dqtz0AvRINL0pKboImN2UXSdR0wPhghMED509FInXXlszKdu0OQcCCCDgbwJmIQkzD8/sl2MW9ngpO5veCX9rJMoTcAIEEgHXZIFRYOc+ELePGVOzCpP5ixBHcAqYvSjMKk9mxS3T5mYPEFZLCc62plYIBLqA+Xn1Wk6Ojh49au2bw/DMQG9Ryt+SAgQSLakfhHmbsadmDKpZKcMc5oe1CSDMCkAcwS3gXOXJtLk5zHuA8cjB3ebUDoFAFTC9Ew88+KAWL12qmdOn68mFC+mdCNTGpNwtKkAg0aL8wZW5GS9/V3Ky9u7dK7NSBvtABFf71rc2zn0ozHvAvBfMe8K8NzgQQAABfxMwG3Ga3tTzz4+0eie2bNnib0WkPAj4tQCTrf26eQKjcGZM/B9XrJCZSP3Qww/L/GDmQMCslmLGI5thA2YPirfefFP3TJnSoOUXUUQAAQSaW8D0ppo/fF0/8Ho9kpKi/G3bmjtL0kcgaATokQiapvR9RcwwJjNZzTkP4oXMTIII3zeD3+doAkszyd51/gTLL/p9s1FABEJOIDY2Vub3WOfOnUOu7lQYgcYKEEg0Vi7E7zNDVYYOGWJNVmMeRIi/GepZfTNXxrxX/vWvcuu9w3CnesJxGQII+EzA9E6MGTvWZ/mREQKBLsDQpkBvQR+X36zEY9bhNsOYzCQ1hjH5uAECPDvnBMfhI0ZYQwgY7hTgDUrxEUAAAQRCWoAeiZBu/vpX3rka01Xxv7WGqDCMqf52XHm6gBlC4BzuZHabZT330404gwACCCCAgL8LEEj4ewv5QfnMrtTO1Zi2F+xkOVc/aJNgKYIZ7vR+4Qc6ePCg9R4z7zUOBBBAAAEEEAgMAYY2BUY7tUgpTS9EVmaWXl33Jz2ckiKziQ8HAk0t4Nxt1syZMLvNDrnpJk297z72HmlqaNJDAAEEEECgiQXokWhi0GBJzizZaSZTm4mxZo1tgohgaVn/rUffvn2t95opoXnvMRnbf9uKkiGAAAIIIGAE6JHgfVBLwPRCPLN8uTa+/TaTqWvJ8MQXAmbFFLPbrOtk7PtnzZLpteBAAAEEEEAAAf8SoEfCv9qjRUvj7IUwO3yaXghWZGrR5gjpzF3Xc7955Eix22xIvx2oPAIIIICAnwrQI+GnDePLYjl7IQo/+EDPr1wp8yGOA4GWFnCu537V1VfX7DZL70RLtwr5I4AAAgggcEqAHolTFiH5yNkL0b59e2tHT4KIkHwb+HWl6Z3w6+ahcAgggAACISxAj0SINj69ECHa8AFabXonArThKDYCCCCAQFAL0CMR1M3ruXLOXgjzqtlYjl4Iz06c9T8Beif8r00oEQIIIIBA6ArQIxFCbe/shWBFphBq9CCsqqfeiTkpKew7EYRtTZUQQAABBPxbgB4J/26fJiud2THYrM1vDlZkajJWEmpBAWfvxCWXXGq9t01PGwcCCCCAAAII+E6AHgnfWbdITqYXImf9eq1etYp9IVqkBci0OQVM78Td99ytvtf01czp09kVuzmxSRsBBBBAAAE3AXok3ECC6emRI0d0V3KyDh48qNdyctgXIpgal7rUEjB7npieNnOYnjfTA8eBAAIIIIAAAs0rQI9E8/q2WOp5ubmaNWOmnlu1UgMHDmyxcpAxAr4SML0TZlfs38THa/LEiRo/YYJGjhrF3AlfNQD5IIAAAgiEnAA9EkHW5CdOnNC9U6Zo06ZN2l6wkyAiyNqX6pxZwATOpgfO9MT9YdYsmZ45DgQQQAABBBBoegECiaY3bbEUt2zZoptHjtQ111yjZ1esUIcOHVqsLGSMQEsKtG7dWvMfe0yDBg3SgIR+Mj10HAgggAACCCDQtAIMbWpazxZJzbmsa+EHH+j5lSvZF6JFWoFM/VEgafhwXdm7txY89pj27t2r+2fNkgkyOBBAAAEEEEDg7AXokTh7wxZNwXVZVzaXa9GmIHM/FTA9c08tWqTOnTtbPXa7d+/205L6R7GMz71T7pUZJsmBAJjOkqYAACAASURBVAKhLvCjbJljFZOUKZvDFxYOleenqUfUWGXZfvRFhg3Ow2HL1IioAUrNP97ge4PxBnokArRVfbGsq/kg8fJLL+v999/Tr371K/1+2DAlJiYGqBjFDmUB103szETsITfdpKn33cdEbJc3hQkgHp07V19/9bXOPfdcffvtt2fVe/P2W29p/WvrrRyuu/46Jr67WPMQAQQQCBYBAokAbEkzedQM1fjlL39pTSptjqEaJo//HHKT/lVeXiP09htvKnn8XZr90EM153iAQCAJmE3szDKxzyxfbi0Ty1BAyTWA+KGiwmrOi9pedFbNest//Zc+/fiA/v3vf1vpbN+2TXl5ecpau5bg7axkuRkBBBDwLwGGNvlXe5yxNGZCtZk8aiaRmsmkzRFEmEI8vWhRrSDCnPu///s/Za5+gVVwzthKXODPAs5lYh9OSbGWiX0pO9ufi9tsZTMBxJDBgzVp/ATZij6XM4g42wzz8/NrBRHO9Ar37tOLa9c6n/IdAQQCVsAhuy1fWSlJionqpJiorhqakql8m/MPj87hSe7Df44rP2WAYrqkKb+8epyUo0yFuYs1qYtJp5N6TFiqTR8erS1jtyk/M0VDrbzMdUlKzcyXzW7ScOY1Vmvyt2r5hL7VZUpS6ot7VVZrONZJlRW+rNQhXU9dU5OOM0tzTa6W1KTTSTFDUpSVb5Pdeclp38tVlHmPenSZqOV7y1SV5ZnyqrYYkqI1iyeqh6mbq8tpefjvCXokWrBtiksPNTj3uydMtO4xe0SYL3O4pmP+I3o6XK8xr3u6zvWavJwNnpKxgoldBQX6r1tusV4/Uzre8jLnXfPzlE5jrvGWn2tezX1NY8pdn/o3d7nrYxSMdUtLSZX5Csa6WZWq/sfZvqa30fwxoq7jy0OlGnLDoLouadRrCx9/QubLHM7yOBPy9H/A2zXu551p8B0BBJpbwCF70cu6f8Sz0t1Pa+cXfdVOZdr3TKruuuEN3ZWzWjPiI+tZiO9UuPRe3bKpmxbl7df/xkbIbntdGdNWqUK/qU7jOxWufEjTPh2hP39SoriIMDnKturRcffrQb2i9cmx1dcV6LEp52l61gZ9vuoiVVjpTNb4489r3czeitBJHc2drRsftmti1lZ93rudwuyfKmvGBI16b7b+8uxwtQ9zyF74vMaP/Vg3Wum0U5hOqiz/SY1Pfkj/tOp2gVvdTBAxW/+1UJq1YZHujDN1r09e1ckc3Krdt67SrtJnZbeVKSIyAP++X1l9RF8W5XzIdz8VMG1UUVHhk9KZvLx95W7Y4JMykAkCvhIw7+lrBwyo3Lx5s6+ybLF8vv7668obBw2q7Na5i9f/49clJlZ+/vnnjSrj7Acf9Jru7WPHNipNbkKgMQJn87nmbO5tTFn96Z7adf+h8vM1Yyqjh62p/PwnU8p/VG6b07+y+90bKo9Yz50lrzpfdd1Pld9ve6Sy+2X9K1O2/cN5Qc290Z0fqdz2/U+Vld9vq0zp7H6N894xlZmf/1BZ+dPfKjOH/aZy+Jq/VdbKriZV5/V9Ku/Z8KXLNdXna+XV5fR0apWhum5ztlV+X5N+5Wll+OnzNZXDrbqVVP5tzd2V3TvfXZn5N5c7rDTrl1eNhWt+fvy49nujqqABGPq4BYMB/NTTX+DOVB0zLMMXx823VvU4uOd1Xvh51nKa7ud5jkAgC5hlYs18idUrVyplzhyZxQyC9TCrWG185x397+pVio27QueFhzdpVW8cMkQ///nPPaY5ePBgj+c5iQACASJQ/om25hxX9NWd1a7WJ8gIdYi5VLId0hFryNGZ6uNQeeE25VVcqpgOES4XhymiQydFO8+EtVX3xE46sPBFvbE3X3lehxhF6+quF+lUkarTqcjX1sLj1Xm1UbeoC12ukRRxsWJijytvyycqVxslzt+uj+fH61j+G9b+Q3m5Lyh16Eil76+a7+Uslul1OLZlue6fu0PRD87Q7VZPhHnVWa8z5XUqpUB/dMo80GtC+ZtU4L5p0/SLC2p34ZkPHGPvuION7ppUmsT8RcBMxDZLKP/iF7+wJmLv37/fX4rWLOXo27dvswQUZmW33/bufVowEd/7SmvlpmapDIkigIBPBBzHSvVJ1ZoMnvOrKNGXx056fq3W2ZM6VlqiupKquvwCxc9co40rrtR3eYs1K3mQep02J6NWwm5PjuuT0m+r5y0c1ivJvavnR1TNyYi5/Eal73eWwgzbytakLj01JHmV9n1nZjv8StcveUGpPaWS4m9c5kmU6d3sL9Rj7FUqWfic3jjqXucz5eVWzAB+yhyJAG685iy6+avl5ne36rU//1n793+s88+PkPmrrfnwwYFAsAo4J2IPGjxYM6dP1/gJE4J+2VJnQOG6elP5985Jk41r6bXZL8pMuv7zq3+2Ehh4w0DdeOONrNjUOE7uQsBvBMLaRqlbuPSJtxKFR+uytq2kI94ucJ5vpbZR0QpXifNEHd8jFZs43Pq6c76ZxPy2/rQiQxOSDmnVnlTF13Gn5NozkKDUzat0Z+y5nu9wFCnrwce1Z8Bi7bDmTFRfVp6vVFuF1N31to66LXO10vt/q18fGKnU9AHq7XqPzpCXgmcPCnokXN8XPK4lYFaEmjR5sp5d8ayeyMggiKilw5NgFujZs6e1tPLBgwd1V3JySKxU5gwozJCnq/r00YUXXnhWTWx6JszPDvM1YsQIgoiz0uRmBPxEILKbrh/ZRiXvHXRbEcmuI8VfSbGd1CHiZ7WHJ3ksepgi469VUvhXKj7iuh6SQ/Yjh+oIL1qpXfww3TV2kMJr9X54SSc8UdfHt6nOq0Tvffr36t6J6kLZ92rJkHiNyCySw/6Nim06bdiWw/6dvvVYB0lhsRqVdrcu3bhYf9xhggNnvc6Ql7f0AvA8gUQANhpFRgCB5hcwgbRZYvm/b7vNWuUoLze3+TP1gxxMQGE+/DfX0tJ+UEWKgAACjRZorStvn6g+2zM095nd1cGEWbkoVdOy22hq2nDFhklh0X01vOdx5WX/RUXWnIly2XKX68nsw6dyjrxG9yyIV96UVGUVmV5Qs6zs63oy47VTQ55ML0FSvIam5FYv9yrJbtO2LR9JQ27WDdHO3oXDeiVjufKsJWirVpb6w5RN6rdgvPqblZCsvPpo58Ppeta5RKu9SHlPzNczGqfUm2MVVh0kHVj3mnaUVQ1VcpTt1rOPZGiTc/TTqdJXPwpTRPztSp/eRq9kvKJCU9f65HVaOoF7gkAicNuOkiOAgA8EzJC+7QU7tWnTJt07ZYrMju8cCCCAQGgKhCkibrSezntcCX9/Qv0uN3MN+ur+4qu1bPMazYivnltp/lL/1BLdpWc1tFu0YqJu19p/Xa8HHklwYWul9sPnaf3yLioY0VMxUdHqNe1DxU8ed2oUUVicbn9+lSZd+JZGWel0Uky3ZL114Thlpt2k9jWfYnvotlvjdChjcFU6I7ary/K1Wji8Y/Xk6uq8ViTo749cryvMvg3V6by6ZrLiI0xCbdR/6lOa+9v3NaFPnDWXolfKHl0y9iktGtvRpdzuDy9Qr1tv16Avn1Pqyg9kV33yck8jcJ+fYxZvMsU3KwixNrdvG7Kh5g293re1ITcEglvArOSUs369Vq9aJbOZ3cCBA4O7wtQOgQAXOJvfmWdzb4CzBdjnQbMh3Tz1Sy7RrLrmPwR6o/hJ+T39v6iJ5fykjBSjpQWs8YJd1WNCdnV3pGuBnCsa9NWU3MO1xxm6XsZjBIJQwEzEHjN2bM0ysU8uXBjUy8Q2uAmrf3bEDFle1b1/WgLOHWj5+XEaDScQQACBABUgkAjQhmu2Ykf8VhMeu1uXbnlc91tddC452T/QqhlmRYPZShnm7C50eZ2HCISAgHOZWFPVoUOGKNiXia13k1b/7Ig76Ozed7vT/oFeyHhNGsLPDzcZniKAAAIBK0AgEbBN11wFd04c+rWKlj6hVYXfVWXkOKy8B6bpGd2tzCeHuYxLbK5ykC4C/ivgXCZ28dKl1jKxz/3xOXon5OVnh9WM36lw5RN65stBSk91Hdfsv21MyRBAIBAEwhSZOE8fl2Z7X9Y1EKoRwGUkkAjgxmu+ol+g+OmLtWjIUT0z50UV2n/U0dcXK3Vje0197PbqSUnNlzspIxAoAmaZ2Lc2btTXX39lLRNrs9kCpejNVM4LFD/xIU3t/Lfqnx1mQyeH7IUvKnWpNDU7TUntWzVT3iSLAAIIIOBrAQIJX4sHSn5hHfX71NlVqxDMuEcTZ+xRvyWLNc25IkOg1INyItDMAqZ3wiwTO37iRE2eOFEvZWeHdu+E+xAnMyRyzhpp+kOawM+PZn43kjwCCCDgWwECCd96B1RuYe1vUsqCQfpqS76+YlxzQLUdhfW9gFnF6bWcHDk3sQvd3gkzxGmyVi4ZpK+Wpun+GWnWOu3pE3+rCN83CzkigAACCDSjAIFEM+IGfNKOMu19Z4+1MUzF9u3aW71BS8DXiwog0EwCzk3s6J1opfbDZip9yD/17pbzGBLZTO83kkUAAQRaWoBAoqVbwG/zL1fR2ser5kVk/lFTL9ukWeOf97Kso99WgoIh0CIC9E5ICgvXLy5sJYV3U6+YyBZpBzJFAAEEEGheAQKJ5vUN0NTN5Mgs3T/3I/WZ+6gmJA6yloT1uqxjgNaSYiPQnAL0TjSnLmkjgAACCPiDAIGEP7SCn5XBUbZNT815zpoXMfeOroqoc1lHPys8xUHAzwTonfCzBqE4CCCAAAJNJkAg0WSUQZKQ47DemJeibI3WsjTX9d7Nso6PKnWgWRL2WeUzXyJIGpxq+EKA3glfKJMHAmcv8MMPP8jsC8OBAAL1EyCQqJ9TiFz1nQqXztQsa7+Ie5XYzm2994iuuv1RsyTsKk2b97aOmiXiORBAoN4C7r0T7IpdbzouRKDZBcz/R7Nb/b/+Vd7seZEBAsEicE5lZWWlqUxMVCcVlx4KlnoFRD0aat7Q6wMCgUIiEKIC5kPLzOnTNeSmmzR+wgSZXgsOBBBoOoH6/s48ceKEVq9apY1vvy2zW73ZaLK+9zZdaf0npVCuu/+0gn+WxNN7gx4J/2wrSoUAAkEu4NwV+/zzI3XzyJHasmVLkNeY6iHgfwLm/535/9e+fXtrl3rz/5IDAQTqL/Cz+l/KlQgggAACTSlgdsW++567df3A6/VISoo25OTo4Tlz1KFDh6bMhrQQQMBNwPRCPL1okUqKi/X8ypWKjY11u4KnCCBQHwF6JOqjxDUIIIBAMwqYDzGvrFunQYMG6fYxY/RSdrbMpE8OBBBoeoG83FxdFf9b9e7dWy9kZhJEND0xKYaQAIFECDU2VUUAAf8WSBo+XK/l5OjgwYPWpM/du3f7d4EpHQIBJHDkyBHdO2WKNm3apO0FO2X+v5leQQ4EEGi8AEObGm/HnQgggECTCziXijWTsZ9YsEBvvfmm7pkyheFOTS5NgqEiYHr3ctavtyZUT58xwwogQqXu1BOB5hagR6K5hUkfAQQQaISAmfRphjuZ4RdmuJNZ257hTo2A5JaQFrDZbLorOdnq5TO9faYXggMBBJpOgB6JprMkJQQQQKDJBcwHn9/1769X171qDXfiL6pNTkyCQSwweeJEPZySIrOHS0MPs9QlBwII1C1AIFG3D68igAACLS5ghjs5V3fKyszUn155RdNmzFDfvn1bvGwUAAF/Fnhr48ZGzYNgXy1/blXK5k8CBBL+1BqUBQEEEKhDwKzuNP+xx2QmYS9bssSaP3FncjKrztRhxkuhK0AwELptT819J8AcCd9ZkxMCCCDQJAKmJ8I5f8IM3UiZM0dmRRoOBBBAAAEEfClAIOFLbfJCAAEEmlDAzJ8wQzdcJ2SbjbY4EEAAAQQQ8IUAgYQvlMkDAQQQaCYBsw6+M6C4+OJ21kZbZoUnAopmAidZBBBAAIEaAQKJGgoeIIAAAoEr4Awo3i/8wKqE2bmXgCJw25OSI4AAAoEgQCARCK1EGRFAAIF6CjhXeDIBxfnnR+jmkSOtgII5FPUE5DIEEEAAgXoLEEjUm4oLEUAAgcARMAHFmLFjrTkUZsiT2dTOTMo2G3RxIIAAAggg0BQCBBJNoUgaCCCAgJ8KOIc8mUnZiddeq0dSUnTbrbdaS8j6aZEpFgIIIIBAgAgQSARIQ1FMBBBA4GwETEBhdvc1y8aazezeevNNXZeYqLzcXCZmnw0s9yKAAAIhLMCGdCHc+FQdAQRCU8DsQ2G+zLyJN15/w1rpafKUezRo8GD17NkzNFGoNQIIIIBAgwXokWgwGTcggAACwSHQoUMH3X3P3Tpw8DP9Jj5eTyxYYA17eik7m16K4GhiaoEAAgg0qwA9Es3KS+IIIICA/ws4hz2ZoU/OXgqz2lPnLl00YuRIJSQkyFzDgQACCCCAgKsAPRKuGjxGAAEEQlzA2Uvxbn6+Jk2erA8LC9W9cxc9uXChNUH7hx9+CHEhqo8AAggg4BQgkHBK8B0BBBBAoJaAmS/xwIMPWkOf+v3ud9r5179aQcW9U6Zoy5YtVu9FrRt4ggACCCAQUgLnVFZWVpoax0R1UnHpoZCqfEtXtqHmDb2+petH/gggEJwC+/fv1+5du7U9f5tVwQGJ16pnr57q1asXQ6CCs8mpFQIIIOAxVmCOBG8MBBBAAIEGCZieCvNlJmqbORUHDx60eituv220Bt80RN2797ACi7i4OJmN8TgQQAABBIJTgB6JFmzXhvYwNPT6FqwaWSOAQIgKmJ2zv/zyS2tuReEHH+jYsWO6JiFBvXv31kVt26pNmzaKjY0NUR2qjQACCASugKfPofRIBG57UnIEEEDA7wRMkGC+zApQ5jhx4oS+/fZbffbpp1avRWlpqd55e6N6X32VomNi1LlzZ0VERCiqUyeFh4dbX2bCNwcCCCCAgP8LEEj4fxtRQgQQQCBgBczQJvPl3gthhkRVVFRYAYap3KZ33tH333+vf/7zn1ag4aywM+BwPnd+v3/WLIZNOTH4jgACCLSQAIFEC8GTLQIIIBDKAs5eB/cAw93EGXC4n2fuhbsIzxFAAAHfCxBI+N6cHBFAAAEE6ingDDjqeTmXIYAAAgj4UIB9JHyITVYIIIAAAggggAACCASLAIFEsLQk9UAAAQQQQAABBBBAwIcCBBI+xCYrBBBAAAEEEEAAAQSCRYBAIlhaknoggAACCCCAAAIIIOBDAQIJH2KTFQIIIIAAAggggAACwSJAIOHDljTLGNZ1mI2bfvjhh7ou4TUEEEAAAQQQQAABBPxCgEDCh80wIKGftcurtyyfXrRIBQUF3l7mPAIIIIAAAggggAACfiNAIOHDpvjD7Nl6dd2rHnO02WzaVVCghIQEj69zEgEEEEAAAQQQQAABfxIgkPBha9xy6y16KiPDY69EVmamps+YofPOO8+HJSIrBBBAAAEEEEAAAQQaJ0Ag0Ti3Rt3VunVreeqVcPZGDBo8uFHpchMCCCCAAAIIIIAAAr4WIJDwsbinXgl6I3zcCGSHAAIIIIAAAgggcNYCBBJnTdiwBNx7JeiNaJgfVyOAAAIIIIAAAgj4h8DP/KMYoVUK0ytxVfxvrUrTGxFabU9tEUAAAQQQQACBYBGgR6IFWtLZK2GyNis1MTeiBRqBLBFAAAEEEEAAAQTOSoAeibPia/zNzrkSDV2pKSaqU+Mz5U4EEEAgiASKSw8FUW2oCgIIIBB4AgQSLdRmpldie8FOme/1PfilWV8prkMAAQQQQAABBBBobgECieYWriP9Dh061PEqLyGAAAIIIIAAAggg4L8CzJHw37ahZAgggAACCCCAAAII+K0AgYTfNg0FQwABBBBAAAEEEEDAfwUIJPy3bSgZAggggAACCCCAAAJ+KxBkgYRD5flp6hE1Vlm2HyX9KFvmWMV0SVN+uaPpGsFRpKykeI3ILFITptp05WvulOw2vbs4Q9mWcXNnRvoIIIAAAggggAAC/igQZIGEO/G5ik3OVvFn85QYGeRVda96sz13qHxftmYsPaCfmi0PEkYAAQQQQAABBBDwdwE+Xft7C1E+BBBAAAEEEEAAAQT8UCCwAwlHmQpzF2tSl04yG7X1mLBUmz486sLsPrTJIbstX1kpSdb15p6YISnKyrfJbt11amjUmvytWj6hb/V1SUp9ca/K6hjH5CgrVN7iieph0rS+kpSamS+b3fWmkyorfFmpQ7pWXdNlopZsdeZdVWxH2V5l15Svq4amZCrfVl5dJ2f5btOS3FwtcS9fuRly5CxDX01atrt2mY3Xiyka6ixjrbpLKs9XapeuGvHCVu1zua7HhOV61yqDyX+e+iWvVYUKlH5DZ/VIyZezdC7wPEQAAQQQQAABBBAIcoEADiS+U+HSe3XL899paN5+FZeWaNfsTtq/aZcqvDWa/QOtmpamgpgF+qj0kIpLi7Rz9nl6NXme1tca71+gx6b8SZq8QZ+XluijzeOklydr/NK91QGHWwb2vVo2bqbe+o+7tOkLk+4hfb5nmv5j3f2asfKD6ntO6mjubA0auU6anKOPTLobBuiz++7Qg7mHrbkWjqO5mnrdNO246CHttNLZradj3tO0pDTlHT3pkukePfP8h+o0+52qOmRepcLUW9Svz0J92i+9Ku137pWeu1+Pvl6VthyHlXfvCCVvv0Tz9hRZXh8t+bUKppzKvyqDCh14dJnyzr9d64zRFwVa1mGLJk3LUqFdikxM087MOxSuBKVuPqiP5ycq0qVkPEQAAQQQQAABBBAIDYHADSTKP9KGlcd12+z7lBRrPsqGKSJ2mB6YfbPCvbSd45tPtf3gpUpIiFaEdU0rtUuco7dKs3Vn7Lkud7XToAWpurd3O4XVpPt7fbXyTe07bdK2mTPwpl74MlGjk69Wu2rRsHYJGnNrFxXlf6pvTKeE45A2r9kkjZ2pB4bHKcKkG3ejRo9spU1r3lWJ47h2rFisTbGT9cDUvtXpRCouOV3LRhYqdcUul7/8d3Spdyu1i09QfHi4uj/4B5cy91ZCbLl27vtCdjlUvmO1UjdGa9bsZF3ZrlWVV9xoPbVikHY+vFo7XOoVXlNGc1k7xV/bS+EH39OBb1yDGRcuHiKAAAIIIIAAAgiEnECABhIOlRduU17FpYrpUBUSVLVcmCI6dFK0l2YMu7irBnT+UIuy3ta+/Lddhgy53xCtq7tepFM41elW5Gtr4Qm3i8MUmThPH3+WpiuP7VRebq7ycnOUlXKrhswtqLnWUbJbuful6JiLq4MY81IbJc7fruK8ZMXaP9HWnMMK7x6ltqcylhShDjGXqiJnmwpdPuzXJFyvBydUuCVfFeHRuqytCSKcR131crtGX6n4SNUAMOcrfEcAAQQQQAABBBAIXYGfBWbVT+pYaYn3IUzeKhXRWzP+nKteW/6qvIxFeuWgGQTVQ7fNnak7bu6vWNeYxGMax/VJ6bdy9Hd70f6psmZMUPqWcsWNnaVJV7bWBQPT9WrMQt2y8JCO2B1egxu3lFSRPU7x2e5nJYW7hkfuAZSH6z2dqlirCT3Wenilo7p5OMspBBBAAAEEEEAAAQS8CQRoINFKbaOiFa4Sb/Xyfj4iVonDzdddSjeTj19/Rc89PE6jitdo53z3CME9mTbqFnWhwvStyws/yvba40rf1UeLdmUoqb3zL/7HlZ/ylVTvEMIkGa7uc3O0PjnOpTfEJSszRMn1aUMf90zTxg3Jiq3V4+GSyFkl7pIODxFAAAEEEEAAAQSCXsDbR0o/r3iYIuOvVVK4+3Abh+xHDtU/vDDj/4ffrtEjO6riQKmO1Syw5CXd8ERdH9/azcauI8VfSbE91cWae1D9sqNC3397ak5BWHRfDe8plRR/4zJhu3pVKbOB3rEYXT+yjUreO1h7pSV9p8LFoxSTlClbTfncinDGp60VPzBR4bb9+qzsVJkkh+yFyzW0ZgO/MybEBQgggAACCCCAAAIIWAIBGkhIirxG9yyIV96UVGUVmT+lm6VdX9eTGa95HfLksGVqRFSSUnOLapZ7tdt2ausH0qBx1ym6RuOwXslYrrzqJU/tRS/rD1M2qd+C8ep/2sZ21R/S92/QSzuOVu107SjTvmfSlbqx7NTbLKyTBs8crUuzF+vp/KrrHGUFemndZ4qbPl2jYi9R/ykz1W97huY+41y2tVy23MVKXSpNTRvuvSfhVC5eHoUpsv94pQ/Yo9RHXtA+K5io8sqYs0ay8nedbO4lGeu06zwUhyrsFaG5u3ddRLyGAAIIIIAAAgiEgEDNR+fAq2srtR8+T+uXd1HBiJ6KiYpWr2kfKn7yOHX3Upmw2NH6Y844XfhmsnpZeylEq1fSW7pw8mI9Mqyjy3CiHrrt1jgdyhhcle6I7eqyfK0WDne9xpmJ+ZB+jzLTu2tvcoKuMOl2S9XOS8bohSVjXFaQMitEPaDVObfqp4wbrOuu6LNMP41+Xqun97YmYIe1H6aFeY8r4e9PqN/lZj+Knhr15gWalPOspsVf4Mywcd/DOirpybVa1u9rpfWJq6qXVfdVNfnXN+Gw6EGafue/lH5DV/UY86pKGt1TUt8cuQ4BBBBAAAEEEEDA3wTOqaysrDSFMpuomf0PQvtwbrhWolmbV7ktCRvaMtQeAQQQQAABBBBAIHQFPMUKAdwjEboNSc0RQAABBBBAAAEEEGhpAQKJlm4B8kcAAQQQQAABBBBAIAAFAnT51+aSrt5crrS50iddBBBAAAEEEEAAAQSCQ4AeieBoR2qBAAIIIIAAAggggIBPBQgkfMpNZggggAACCCCAAAIIBIcAgURwtCO1QAABBBBAAAEEEEDApwIEEj7lJjMEEEAAAQQQQAABBIJDIEQDCbOr82YtSVsn21lvplYu29ZnNffFouodnn+ULXOsYrqkKb/8rBM/7V1WtTv3WGXZfjztNe8nTH1zlTqkq7VfSExSpmzlNr27OEPZDUrHew68ggACCCCAAAIIsFC46QAABylJREFUIBBaAiEaSJzQvqz5euajH86+tcsLtfa+Fdr/09kn1WwpOGxa/4c5yot6TDu+OKTivDvUtjBbM5YekD8Xu9k8SBgBBBBAAAEEEEDgrAVCNJA4a7fATODCCxRBiwdm21FqBBBAAAEEEEDAzwRC8GPlceWnjNKE7MPS/nkacvkApeYfr2oWu035mSkaGtWpagjQkBRl5dtk99Zo5flK7TNOr1RU6MDcG3VFreFMR/XRO0s1qUt1Wl0maslWt7QcZSp8sQH5eSmHo2yvslOSqsoc1VVDUzKVbyu3rraGQl1+o9L3V6gie5zio67WXZPGqF/yWlWoQOk3dFaPlHxVXe0lA04jgAACCCCAAAIIIOAmEIKBRBslzl+vVWM7Sj3TtPGL7UpPbCPZP1XWjDs0beclmrenSMWlRdr56CUqmDJcty7e6zmYiExU+p41ui08XN3n/kWffzZPiZHVpBW7tHl/Jz3wfklVWiuitHn8Q1pV+F1VEzgOK+/eEUre7syvRB8t+bUKptyhB3MPV8+3cGstD08dR3M19bpp2nHRQ9pphi2V7tbTMe9pWlKa8o6eVFhssjZ88Rel9gxX+Ng1Kix9Ty/870vamXmHwpWg1M0H9fH8REV6SJtTCCCAAAIIIIAAAgh4EwjBQMIThUPl+17Vol19lP7oXbqyXStJrdSu9yQ9teJmfbV0qdY3dFJy+M164MFhirXGErVSu/4365aeh7T942NyyKHyHauVujFas2YnV+cXpoi40XpqxSDtfHi1dtRrovZx7VixWJtiJ+uBqX3VzmrNSMUlp2vZyEKlrthFT4On5uYcAggggAACCCCAwFkLEEhYhCdUuCVfFbE91cUKIpyuYYro0EnR+krFR7wOcHJeXI/v/1ZJ8Teyqzq/8Ghd1tYELc6jOr+KfG0tPOE86f17+SfamnNY4d2j1LZWS0aoQ8ylqsjZpsJ6BSTes+AVBBBAAAEEEEAAAQQ8CfzM08mQO+f4Vl8eqJ4n4bHyx/VJ6bdyqI1qfV73eG0DTlas1YQeaz3c0FHdPJz1dsqa+5Dt4dXwaA8nOYUAAggggAACCCCAwNkLEEgYw7ALdVn3NtIBb6Bt1C3qwqYNIkxWZo7GhmTFnlV0YuZn5Gh9cpz38jX9dhbeoDiPAAIIIIAAAgggECICZ/URNniMWit+YKLCbfv1WdlJl2o5ZD9ySCW6VDEdIlzOn+3DOvIrXK6hUfXccC6ym64f2UYl7x1UWa1g4TsVLh4la+O5WufPttzcjwACCCCAAAIIIIBAlUCIBhJVcwiqCH6U3e5Q5JW3aNY1e5T6yAvaZwUTDtmLXtYfprymS6dP16jYcz2/ZyIuVkzsz6teq7DLXq8P7mGK7D9e6QPc8rO9row5a6S68qtVijbqP2Wm+m3P0NxndlcHE+Wy5S5W6lJpatpwL70dzrkfJjGHKuwV9V4lqlb2PEEAAQQQQAABBBAIWYEQDSTOVfSN4zT25JMacvlvdftrJXJEdNWdS9ZqWb+vldYnTjFR0eo1429KWJGrdTN7y2t/RFgnDZ45SietfSTu1vqSH+v3ZgrrqKQn3fJLeksXTl6l1dPryM8t9bD2w7Qw73El/P0J9bvc7FnRU6PevECTcp7VtPgL3K4+9TQsepCm3/kvpd/QVT3GvKqSegVAp+7nEQIIIIAAAggggEBoC5xTWVlZaQhiojqpuPRQaGtQewQQQAABBBBAAAEEEDhNwFOsEKI9EqfZcAIBBBBAAAEEEEAAAQQaIEAg0QAsLkUAAQQQQAABBBBAAIEqAQIJ3gkIIIAAAggggAACCCDQYAECiQaTcQMCCCCAAAIIIIAAAggQSPAeQAABBBBAAAEEEEAAgQYLEEg0mIwbEEAAAQQQQAABBBBAgECC9wACCCCAAAIIIIAAAgg0WIBAosFk3IAAAggggAACCCCAAAIEErwHEEAAAQQQQAABBBBAoMECBBINJuMGBBBAAAEEEEAAAQQQIJDgPYAAAggggAACCCCAAAINFiCQaDAZNyCAAAIIIIAAAggggACBBO8BBBBAAAEEEEAAAQQQaLAAgUSDybgBAQQQQAABBBBAAAEECCR4DyCAAAIIIIAAAggggECDBQgkGkzGDQgggAACCCCAAAIIIEAgwXsAAQQQQAABBBBAAAEEGixAINFgMm5AAAEEEEAAAQQQQAABAgneAwgggAACCCCAAAIIINBgAQKJBpNxAwIIIIAAAggggAACCBBI8B5AAAEEEEAAAQQQQACBBgsQSDSYjBsQQAABBBBAAAEEEECAQIL3AAIIIIAAAggggAACCDRYgECiwWTcgAACCCCAAAIIIIAAAudUVlZWxkR1QgIBBBBAAAEEEEAAAQQQqFOguPRQzetWIFHzjAcIIIAAAggggAACCCCAQD0EGNpUDyQuQQABBBBAAAEEEEAAgdoC/z8WL+MoqrgnpQAAAABJRU5ErkJggg=="></p>
</div>

<div class="specification">
<p>X and Y represent the equilibrium positions of two air molecules in the pipe. The arrow&nbsp;represents the velocity of the molecule at Y.</p>
</div>

<div class="specification">
<p>The loudspeaker in (a) now emits sound towards an air–water boundary. A, B and C&nbsp;are parallel wavefronts emitted by the loudspeaker. The parts of wavefronts A and B&nbsp;in water are not shown. Wavefront C has not yet entered the water.</p>
<p><img 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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline how the standing wave is formed.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw an arrow on the diagram to represent the direction of motion of the&nbsp;molecule at X.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Label a position N that is a node of the standing wave.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The speed of sound is 340 m s<sup>–1</sup> and the length of the pipe is 0.30 m.&nbsp;Calculate, in Hz, the frequency of the sound.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The speed of sound in air is 340 m s<sup>–1</sup> and in water it is 1500 m s<sup>–1</sup>.</p>
<p>The wavefronts make an angle <em>θ</em> with the surface of the water. Determine the&nbsp;maximum angle, <em>θ</em><sub>max</sub>, at which the sound can enter water. Give your answer&nbsp;to the correct number of significant figures.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw lines on the diagram to complete wavefronts A and B in water for <em>θ</em> &lt; <em>θ</em><sub>max</sub>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the incident wave <strong>«</strong>from the speaker<strong>» </strong>and the reflected wave <strong>«</strong>from the closed end<strong>»</strong></p>
<p>superpose/combine/interfere</p>
<p>&nbsp;</p>
<p><em>Allow superimpose/add up</em></p>
<p><em>Do not allow meet/interact</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Horizontal arrow from X to the right</p>
<p>&nbsp;</p>
<p><em>MP2 is dependent on MP1</em></p>
<p><em>Ignore length of arrow</em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>P at a node</p>
<p>&nbsp;</p>
<p><img src="images/Schermafbeelding_2018-08-12_om_14.17.43.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/03.a.iii/M"></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>wavelength is&nbsp;<em>λ</em> =&nbsp;<strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4 \times 0.30}}{3}">
  <mfrac>
    <mrow>
      <mn>4</mn>
      <mo>×</mo>
      <mn>0.30</mn>
    </mrow>
    <mn>3</mn>
  </mfrac>
</math></span> =<strong>»</strong> 0.40&nbsp;<strong>«</strong>m<strong>»</strong></p>
<p><em>f</em> =&nbsp;<strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{340}}{{0.40}}">
  <mfrac>
    <mrow>
      <mn>340</mn>
    </mrow>
    <mrow>
      <mn>0.40</mn>
    </mrow>
  </mfrac>
</math></span><strong>»</strong> 850&nbsp;<strong>«</strong>Hz<strong>»</strong></p>
<p>&nbsp;</p>
<p><em>Award </em><strong><em>[2] </em></strong><em>for a bald correct answer</em></p>
<p><em>Allow ECF from MP1</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\sin {\theta _c}}}{{340}} = \frac{1}{{1500}}">
  <mfrac>
    <mrow>
      <mi>sin</mi>
      <mo>⁡</mo>
      <mrow>
        <msub>
          <mi>θ</mi>
          <mi>c</mi>
        </msub>
      </mrow>
    </mrow>
    <mrow>
      <mn>340</mn>
    </mrow>
  </mfrac>
  <mo>=</mo>
  <mfrac>
    <mn>1</mn>
    <mrow>
      <mn>1500</mn>
    </mrow>
  </mfrac>
</math></span></p>
<p><em>θ<sub>c</sub></em> = 13<strong>«</strong>°<strong>»</strong></p>
<p>&nbsp;</p>
<p><em>Award </em><strong><em>[2] </em></strong><em>for a bald correct answer</em></p>
<p><em>Award </em><strong><em>[2] </em></strong><em>for a bald answer of 13.1</em></p>
<p>&nbsp;</p>
<p><em>Answer must be to 2/3 significant figures to award MP2</em></p>
<p><em>Allow 0.23 radians</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct orientation</p>
<p>greater separation</p>
<p>&nbsp;</p>
<p><em>Do not penalize the lengths of A and B in the water</em></p>
<p><em>Do not penalize a wavefront for C if it is consistent with A and B</em></p>
<p><em>MP1 must be awarded for MP2 to be awarded</em></p>
<p><em><img src="images/Schermafbeelding_2018-08-12_om_14.30.57.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/03.b.ii/M"></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<p>&nbsp;</p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A beam of coherent monochromatic light from a distant galaxy is used in an optics experiment on Earth.</p>
</div>

<div class="specification">
<p>The beam is incident normally on a double slit. The distance between the slits is 0.300 mm. A screen is at a distance <em>D </em>from the slits. The diffraction angle <em>θ </em>is labelled.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-10_om_17.53.34.png" alt="M18/4/PHYSI/SP2/ENG/TZ1/03.a"></p>
</div>

<div class="specification">
<p>The graph of variation of intensity with diffraction angle for this experiment is shown.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-13_om_12.36.49.png" alt="M18/4/PHYSI/HP2/ENG/TZ1/03.b"></p>
</div>

<div class="specification">
<p>A beam of coherent monochromatic light from a distant galaxy is used in an optics experiment on Earth.</p>
</div>

<div class="specification">
<p>The beam is incident normally on a double slit. The distance between the slits is 0.300 mm. A screen is at a distance <em>D </em>from the slits. The diffraction angle <em>θ </em>is labelled.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-10_om_17.53.34.png" alt="M18/4/PHYSI/SP2/ENG/TZ1/03.a"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A series of dark and bright fringes appears on the screen. Explain how a dark fringe is formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the beam has to be coherent in order for the fringes to be visible.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The wavelength of the beam as observed on Earth is 633.0 nm. The separation between a dark and a bright fringe on the screen is 4.50 mm. Calculate <em>D</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the angular separation between the central peak and the missing peak in the double-slit interference intensity pattern. State your answer to an appropriate number of significant figures.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce, in mm, the width of one slit.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The wavelength of the light in the beam when emitted by the galaxy was 621.4 nm.</p>
<p>Explain, without further calculation, what can be deduced about the relative motion of the galaxy and the Earth.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>superposition of light from each slit / interference of light from both slits</p>
<p>with path/phase difference of any half-odd multiple of wavelength/any odd multiple of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi ">
  <mi>π</mi>
</math></span>&nbsp;(in words or symbols)</p>
<p>producing destructive interference</p>
<p>&nbsp;</p>
<p><em>Ignore any reference to crests and troughs.</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>light waves (from slits) must have constant phase difference / no phase difference / be in phase</p>
<p>&nbsp;</p>
<p><em>OWTTE</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of solving for <em>D&nbsp;</em>«<em>D</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{sd}}{\lambda }">
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mi>s</mi>
      <mi>d</mi>
    </mrow>
    <mi>λ</mi>
  </mfrac>
</math></span>» ✔</p>
<p>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4.50 \times {{10}^{ - 3}} \times 0.300 \times {{10}^{ - 3}}}}{{633.0 \times {{10}^{ - 9}}}} \times 2">
  <mfrac>
    <mrow>
      <mn>4.50</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>3</mn>
          </mrow>
        </msup>
      </mrow>
      <mo>×</mo>
      <mn>0.300</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>3</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mn>633.0</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>9</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
  <mo>×</mo>
  <mn>2</mn>
</math></span>» = 4.27 «m»&nbsp;✔</p>
<p>&nbsp;</p>
<p><em>Award <strong>[1]</strong> max for 2.13 m.</em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>sin&nbsp;<em>θ</em> =&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4 \times 633.0 \times {{10}^{ - 9}}}}{{0.300 \times {{10}^{ - 3}}}}">
  <mfrac>
    <mrow>
      <mn>4</mn>
      <mo>×</mo>
      <mn>633.0</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>9</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mn>0.300</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>3</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
</math></span></p>
<p>sin&nbsp;<em>θ</em> =&nbsp;0.0084401…</p>
<p>final answer to three sig figs (<em>eg </em>0.00844 or 8.44 × 10<sup>–3</sup>)</p>
<p>&nbsp;</p>
<p><em>Allow ECF from (a)(iii).</em></p>
<p><em>Award </em><strong><em>[1] </em></strong><em>for 0.121 rad (can award MP3 in addition for proper sig fig)</em></p>
<p><em>Accept calculation in degrees leading to 0.481 degrees.</em></p>
<p><em>Award MP3 for any answer expressed to 3sf.</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of diffraction formula&nbsp;<strong>«</strong><em>b</em>&nbsp;= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\lambda }{\theta }">
  <mfrac>
    <mi>λ</mi>
    <mi>θ</mi>
  </mfrac>
</math></span><strong>»</strong></p>
<p><strong><em>OR</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{633.0 \times {{10}^{ - 9}}}}{{0.00844}}">
  <mfrac>
    <mrow>
      <mn>633.0</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>9</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mn>0.00844</mn>
    </mrow>
  </mfrac>
</math></span></p>
<p><strong>«</strong>=<strong>»</strong>&nbsp;7.5<strong>«</strong>00<strong>»</strong>&nbsp;× 10<sup>–2</sup><strong>&nbsp;«</strong>mm<strong>»</strong></p>
<p>&nbsp;</p>
<p><em>Allow ECF from (b)(i).</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>wavelength increases (so frequency decreases) / light is redshifted</p>
<p>galaxy is moving away from Earth</p>
<p>&nbsp;</p>
<p><em>Allow ECF for MP2 (ie wavelength decreases so moving towards).</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">The diagram shows the direction of a sound wave travelling in a metal sheet.</span></p>
<p><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
</div>

<div class="specification">
<p><span style="background-color: #ffffff;">The sound wave in air in (c) enters a pipe that is open at both ends. The diagram shows the displacement, at a particular time <em>T</em>, of the standing wave that is set up in the pipe.</span></p>
<p><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">A particular air molecule has its equilibrium position at the point labelled M.</span></span></p>
</div>

<div class="specification">
<p><span style="background-color: #ffffff;">Sound of frequency <em>f</em> = 2500 Hz is emitted from an aircraft that moves with speed <em>v</em> = 280 m s<sup>–1 </sup>away from a stationary observer. The speed of sound in still air is <em>c</em> = 340 m s<sup>–1</sup>.</span></p>
<p><span style="background-color: #ffffff;"><img 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"></span></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Particle P in the metal sheet performs simple harmonic oscillations. When the displacement of P is 3.2 μm the magnitude of its acceleration is 7.9 m s<sup>-2</sup>. Calculate the magnitude of the acceleration of P when its displacement is 2.3 μm.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The wave is incident at point Q on the metal–air boundary. The wave makes an angle of 54° with the normal at Q. The speed of sound in the metal is 6010 m s<sup>–1</sup> and the speed of sound in air is 340 m s<sup>–1</sup>. Calculate the angle between the normal at Q and the direction of the wave in air.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The frequency of the sound wave in the metal is 250 Hz. Determine the wavelength of the wave in air.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">On the diagram, at time <em>T</em>, draw an arrow to indicate the acceleration of this molecule.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">di.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">On the diagram, at time <em>T</em>, label with the letter C a point in the pipe that is at the centre of a compression.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">dii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Calculate the frequency heard by the observer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ei.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Calculate the&nbsp;wavelength measured by the observer.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">eii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">Expression or statement showing acceleration is proportional to displacement ✔</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">so </span><span style="background-color:#ffffff;">«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7.9 \times \frac{{2.3}}{{3.2}}">
  <mn>7.9</mn>
  <mo>×</mo>
  <mfrac>
    <mrow>
      <mn>2.3</mn>
    </mrow>
    <mrow>
      <mn>3.2</mn>
    </mrow>
  </mfrac>
</math></span>» = 5.7«ms<sup>–2</sup>»&nbsp;<span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sin \theta&nbsp; = \frac{{340}}{{6010}} \times \sin {54^0}">
  <mi>sin</mi>
  <mo>⁡</mo>
  <mi>θ</mi>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>340</mn>
    </mrow>
    <mrow>
      <mn>6010</mn>
    </mrow>
  </mfrac>
  <mo>×</mo>
  <mi>sin</mi>
  <mo>⁡</mo>
  <mrow>
    <msup>
      <mn>54</mn>
      <mn>0</mn>
    </msup>
  </mrow>
</math></span></span><span style="background-color:#ffffff;"> &nbsp; ✔</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta&nbsp; = {2.6^0}">
  <mi>θ</mi>
  <mo>=</mo>
  <mrow>
    <msup>
      <mn>2.6</mn>
      <mn>0</mn>
    </msup>
  </mrow>
</math></span> &nbsp;&nbsp;<span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda&nbsp; =&nbsp;« \frac{{340}}{{250}} =» 1.36 \approx 1.4 «{\text{m}}»">
  <mi>λ</mi>
  <mo>=</mo>
  <mrow>
    <mo>«</mo>
  </mrow>
  <mfrac>
    <mrow>
      <mn>340</mn>
    </mrow>
    <mrow>
      <mn>250</mn>
    </mrow>
  </mfrac>
  <mo>=</mo>
  <mrow>
    <mo>»</mo>
  </mrow>
  <mn>1.36</mn>
  <mo>≈</mo>
  <mn>1.4</mn>
  <mrow>
    <mo>«</mo>
  </mrow>
  <mrow>
    <mtext>m</mtext>
  </mrow>
  <mrow>
    <mo>»</mo>
  </mrow>
</math></span></span><span style="background-color:#ffffff;">&nbsp; ✔</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">horizontal arrow «at M» pointing left ✔</span></p>
<div class="question_part_label">di.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">any point labelled C on the vertical line shown below ✔</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><em>eg</em>:</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><img 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" width="416" height="175"></span></p>
<div class="question_part_label">dii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f' = 2500 \times \frac{{340}}{{340 + 280}}">
  <msup>
    <mi>f</mi>
    <mo>′</mo>
  </msup>
  <mo>=</mo>
  <mn>2500</mn>
  <mo>×</mo>
  <mfrac>
    <mrow>
      <mn>340</mn>
    </mrow>
    <mrow>
      <mn>340</mn>
      <mo>+</mo>
      <mn>280</mn>
    </mrow>
  </mfrac>
</math></span> &nbsp; ✔</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f' = 1371 \approx 1400">
  <msup>
    <mi>f</mi>
    <mo>′</mo>
  </msup>
  <mo>=</mo>
  <mn>1371</mn>
  <mo>≈</mo>
  <mn>1400</mn>
</math></span>«Hz» &nbsp;&nbsp;✔</span></span></p>
<div class="question_part_label">ei.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ' = \frac{{340}}{{1371}} \approx 0.24/0.25">
  <msup>
    <mi>λ</mi>
    <mo>′</mo>
  </msup>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>340</mn>
    </mrow>
    <mrow>
      <mn>1371</mn>
    </mrow>
  </mfrac>
  <mo>≈</mo>
  <mn>0.24</mn>
  <mrow>
    <mo>/</mo>
  </mrow>
  <mn>0.25</mn>
</math></span>«m» &nbsp;✔</span></p>
<div class="question_part_label">eii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This was well answered at both levels.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many scored full marks on this question. Common errors were using the calculator in radian mode or getting the equation upside down.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was very well answered.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Very few candidates could interpret this situation and most arrows were shown in a vertical plane.</p>
<div class="question_part_label">di.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was answered well at both levels.</p>
<div class="question_part_label">dii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was answered well with the most common mistake being to swap the speed of sound and the speed of the aircraft.</p>
<div class="question_part_label">ei.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Answered well with ECF often being awarded to those who answered the previous part incorrectly.</p>
<div class="question_part_label">eii.</div>
</div>
<br><hr><br><div class="specification">
<p>Titan is a moon of Saturn. The Titan-Sun distance is 9.3 times greater than the&nbsp;Earth-Sun distance.</p>
</div>

<div class="specification">
<p>The molar mass of nitrogen is 28&thinsp;g&thinsp;mol<sup>&minus;1</sup>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the intensity of the solar radiation at the location of Titan is 16 W m<sup>−2</sup>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Titan has an atmosphere of nitrogen. The albedo of the atmosphere is 0.22. The surface of Titan may be assumed to be a black body. Explain why the <strong>average </strong>intensity of solar radiation <strong>absorbed</strong> by the whole surface of Titan is 3.1 W m<sup>−2</sup>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the equilibrium surface temperature of Titan is about 90 K.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The mass of Titan is 0.025 times the mass of the Earth and its radius is 0.404 times the radius of the Earth. The escape speed from Earth is 11.2 km s<sup>−1</sup>. Show that the escape speed from Titan is 2.8 km s<sup>−1</sup>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The orbital radius of Titan around Saturn is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> and the period of revolution is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>.</p>
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>T</mi><mn>2</mn></msup><mo>=</mo><mfrac><mrow><mn>4</mn><msup><mi mathvariant="normal">π</mi><mn>2</mn></msup><msup><mi>R</mi><mrow><mo> </mo><mn>3</mn></mrow></msup></mrow><mrow><mi>G</mi><mi>M</mi></mrow></mfrac></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math> is the mass of Saturn.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The orbital radius of Titan around Saturn is 1.2 × 10<sup>9 </sup>m and the orbital period is 15.9 days. Estimate the mass of Saturn.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the mass of a nitrogen molecule is 4.7 × 10<sup>−26</sup> kg.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the root mean square speed of nitrogen molecules in the Titan atmosphere. Assume an atmosphere temperature of 90 K.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Discuss, by reference to the answer in (b), whether it is likely that Titan will lose its atmosphere of nitrogen.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>incident intensity <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1360</mn><mrow><mn>9</mn><mo>.</mo><msup><mn>3</mn><mn>2</mn></msup></mrow></mfrac></math> <em><strong>OR </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>.</mo><mn>7</mn><mo>≈</mo><mn>16</mn></math> «W m<sup>−2</sup>» ✓</p>
<p> </p>
<p><em>Allow the use of 1400 for the solar constant.</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>exposed surface is ¼ of the total surface ✓</p>
<p>absorbed intensity = (1−0.22) × incident intensity ✓</p>
<p>0.78 × 0.25 × 15.7  <em><strong>OR </strong> </em>3.07 «W m<sup>−2</sup>» ✓</p>
<p> </p>
<p><em>Allow 3.06 from rounding and 3.12 if they use 16</em> W m<sup>−2</sup>.</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>σT </em><sup>4</sup> = 3.07</p>
<p><em><strong>OR</strong></em></p>
<p><em>T</em> = 86 «K» ✓</p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mo>«</mo><msqrt><mfrac><mrow><mn>2</mn><mi>G</mi><mi>M</mi></mrow><mi>R</mi></mfrac></msqrt><mo>=</mo><mo>»</mo><msqrt><mfrac><mrow><mn>0</mn><mo>.</mo><mn>025</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>404</mn></mrow></mfrac></msqrt><mo>×</mo><mn>11</mn><mo>.</mo><mn>2</mn></math></p>
<p><em><strong>OR</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>79</mn></math> «km s<sup>−1</sup>» ✓</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct equating of gravitational force / acceleration to centripetal force / acceleration ✓</p>
<p>correct rearrangement to reach the expression given ✓</p>
<p> </p>
<p><em>Allow use of <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mi>G</mi><mi>M</mi></mrow><mi>R</mi></mfrac></msqrt><mo>=</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi><mi>R</mi></mrow><mi>T</mi></mfrac></math> for <strong>MP1</strong>.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mn>15</mn><mo>.</mo><mn>9</mn><mo>×</mo><mn>24</mn><mo>×</mo><mn>3600</mn></math> «s» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mfrac><mrow><mn>4</mn><msup><mi mathvariant="normal">π</mi><mn>2</mn></msup><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></mrow></mfenced><mn>3</mn></msup></mrow><mrow><mn>6</mn><mo>.</mo><mn>67</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>×</mo><msup><mfenced><mrow><mn>15</mn><mo>.</mo><mn>9</mn><mo>×</mo><mn>24</mn><mo>×</mo><mn>3600</mn></mrow></mfenced><mn>2</mn></msup></mrow></mfrac><mo>=</mo><mn>5</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>26</mn></msup><mo> </mo></math>«kg» ✓</p>
<p> </p>
<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong>.</em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mfrac><mrow><mn>28</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow><mrow><mn>6</mn><mo>.</mo><mn>02</mn><mo>×</mo><msup><mn>10</mn><mn>23</mn></msup></mrow></mfrac></math></p>
<p><em><strong>OR</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>65</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>26</mn></mrow></msup></math> «kg» ✓</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mi>k</mi><mi>T</mi><mo>⇒</mo><mo>»</mo><mi>v</mi><mo>=</mo><msqrt><mfrac><mrow><mn>3</mn><mi>k</mi><mi>T</mi></mrow><mi>m</mi></mfrac></msqrt></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mo>«</mo><msqrt><mfrac><mrow><mn>3</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>38</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>23</mn></mrow></msup><mo>×</mo><mn>90</mn></mrow><mrow><mn>4</mn><mo>.</mo><mn>651</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>26</mn></mrow></msup></mrow></mfrac></msqrt><mo>=</mo><mo>»</mo><mn>283</mn><mo>≈</mo><mn>300</mn></math> «ms<sup>−1</sup>» ✓</p>
<p> </p>
<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>
<p><em>Allow 282 from a rounded mass.</em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>no, molecular speeds much less than escape speed ✓</p>
<p> </p>
<p><em>Allow <strong>ECF</strong> from incorrect <strong>(d)(ii)</strong>.</em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A vertical solid cylinder of uniform cross-sectional area <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> floats in water. The cylinder is partially submerged. When the cylinder floats at rest, a mark is aligned with the water surface. The cylinder is pushed vertically downwards so that the mark is a distance <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> below the water surface.</p>
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" width="509" height="210"></p>
<p style="text-align: left;">At time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math> the cylinder is released. The resultant vertical force <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math> on the cylinder is related to the displacement <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> of the mark by</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mo>-</mo><mi>ρ</mi><mi>A</mi><mi>g</mi><mi>x</mi></math></p>
<p style="text-align: left;">where&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ρ</mi></math>&nbsp;is the density of water.</p>
</div>

<div class="specification">
<p>The cylinder was initially pushed down a distance <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>250</mn><mo> </mo><mi mathvariant="normal">m</mi></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the cylinder performs simple harmonic motion when released.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The mass of the cylinder is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>118</mn><mo> </mo><mi>kg</mi></math> and the cross-sectional area of the cylinder is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>29</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo> </mo><msup><mi mathvariant="normal">m</mi><mn>2</mn></msup></math>. The density of water is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>03</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo> </mo><mi>kg</mi><mo> </mo><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn>3</mn></mrow></msup></math>. Show that the angular frequency of oscillation of the cylinder is about <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>4</mn><mo> </mo><mo> </mo><mi>rad</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the maximum kinetic energy <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>kmax</mi></msub></math> of the cylinder.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw, on the axes, the graph to show how the kinetic energy of the cylinder varies with time during <strong>one</strong> period of oscillation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>.</p>
<p><img style="display: block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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" width="610" height="371"></p>
<div class="marks">[2]</div>
<div class="question_part_label">c(ii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">the </span><span class="fontstyle2">«</span><span class="fontstyle0">restoring</span><span class="fontstyle2">» </span><span class="fontstyle0">force/acceleration is proportional to displacement </span><span class="fontstyle3">✓ </span></p>
<p><em><span class="fontstyle4"><br>Allow use of symbols i.e. </span><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>∝</mo><mo>-</mo><mi>x</mi></math><span class="fontstyle4"> or </span><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>∝</mo><mo>-</mo><mi>x</mi></math></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">Evidence of equating <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><msup><mi>ω</mi><mn>2</mn></msup><mi>x</mi><mo>=</mo><mi>ρ</mi><mi>A</mi><mi>g</mi><mi>x</mi></math> «to obtain <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>ρ</mi><mi>A</mi><mi>g</mi></mrow><mi>m</mi></mfrac><mo>=</mo><msup><mi>ω</mi><mn>2</mn></msup></math>» ✓</span></p>
<p> </p>
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ω</mi><mo>=</mo><msqrt><mfrac><mrow><mn>1</mn><mo>.</mo><mn>03</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo>×</mo><mn>2</mn><mo>.</mo><mn>29</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>×</mo><mn>9</mn><mo>.</mo><mn>81</mn></mrow><mn>118</mn></mfrac></msqrt></math> <em><strong>OR </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>43</mn><mo>«</mo><mi>rad</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> ✓</span></p>
<p> </p>
<p><em><span class="fontstyle0">Answer to at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="italic">3</mn></math> s.f.</span></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">«<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi mathvariant="normal">K</mi></msub></math> </span><span class="fontstyle1">is a maximum when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn></math> hence</span><span class="fontstyle0">» <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mrow><mi mathvariant="normal">K</mi><mo>,</mo><mo> </mo><mi>max</mi></mrow></msub><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>118</mn><mo>×</mo><mn>4</mn><mo>.</mo><msup><mn>4</mn><mn>2</mn></msup><mfenced><mrow><mn>0</mn><mo>.</mo><msup><mn>250</mn><mn>2</mn></msup><mo>-</mo><msup><mn>0</mn><mn>2</mn></msup></mrow></mfenced></math> </span><span class="fontstyle3">✓</span></p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>71</mn><mo>.</mo><mn>4</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">J</mi><mo>»</mo></math> <span class="fontstyle3">✓</span></p>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">energy never negative </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">correct shape with two maxima </span><span class="fontstyle2">✓</span></p>
<p><img src="data:image/png;base64,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"></p>
<div class="question_part_label">c(ii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This was well answered with candidates gaining credit for answers in words or symbols.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Again, very well answered.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>A straightforward calculation with the most common mistake being missing the squared on the omega.</p>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most candidates answered with a graph that was only positive so scored the first mark.</p>
<div class="question_part_label">c(ii).</div>
</div>
<br><hr><br><div class="specification">
<p>Two loudspeakers A and B are initially equidistant from a microphone M. The frequency and&nbsp;intensity emitted by A and B are the same. A and B emit sound in phase. A is fixed in position.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>B is moved slowly away from M along the line MP. The graph shows the variation with&nbsp;distance travelled by B of the received intensity at M.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the received intensity varies between maximum and minimum values.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain the wavelength of the sound measured at M.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>B is placed at the first minimum. The frequency is then changed until the received intensity is again at a maximum.</p>
<p>Show that the lowest frequency at which the intensity maximum can occur is about 3 kHz.</p>
<p style="text-align:center;">Speed of sound = 340 m s<sup>−1</sup></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Loudspeaker A is switched off. Loudspeaker B moves away from M at a speed of 1.5 m s<sup>−1</sup> while emitting a frequency of 3.0 kHz.</p>
<p>Determine the difference between the frequency detected at M and that emitted by B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>movement of B means that path distance is different « between BM and AM »<br><em><strong>OR</strong></em><br>movement of B creates a path difference «between BM and AM» ✓</p>
<p>interference<br><em><strong>OR</strong></em><br>superposition «of waves» ✓</p>
<p>maximum when waves arrive in phase / path difference = n x lambda<br><em><strong>OR</strong></em><br>minimum when waves arrive «180° or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>π</mi></math> » out of phase / path difference = (n+½) x lambda ✓</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>wavelength = 26 cm ✓</p>
<p><br>peak to peak distance is the path difference which is one wavelength</p>
<p><em><strong>OR</strong></em></p>
<p>this is the distance B moves to be back in phase «with A» ✓</p>
<p> </p>
<p><em>Allow 25 – 27 cm for <strong>MP1</strong>.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>λ</mi><mn>2</mn></mfrac></math>» = 13 cm ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo></math>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>c</mi><mi>λ</mi></mfrac><mo>=</mo><mfrac><mn>340</mn><mrow><mn>0</mn><mo>.</mo><mn>13</mn></mrow></mfrac><mo>=</mo></math>» 2.6 «kHz» ✓</p>
<p> </p>
<p><em>Allow ½ of wavelength from (b) or data from graph for <strong>MP1</strong>.</em></p>
<p><em>Allow ECF from <strong>MP1</strong>.</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em><br>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mo>=</mo><mi>f</mi><mfrac><mi>v</mi><mrow><mi>v</mi><mo>+</mo><msub><mi>u</mi><mn>0</mn></msub></mrow></mfrac></math> (+ sign must be seen) <strong><em>OR</em> </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo></math>= 2987 «Hz» ✓<br>« <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Δ</mi><mi>f</mi></math>» = 13 «Hz» ✓</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em><br>Attempted use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>Δ</mi><mi>f</mi></mrow><mi>f</mi></mfrac></math>≈ <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>v</mi><mi>c</mi></mfrac></math><br><br>« Δf » = 13 «Hz» ✓</p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This was an "explain" questions, so examiners were looking for a clear discussion of the movement of speaker B creating a changing path difference between B and the microphone and A and the microphone. This path difference would lead to interference, and the examiners were looking for a connection between specific phase differences or path differences for maxima or minima. Some candidates were able to discuss basic concepts of interference (e.g. "there is constructive and destructive interference"), but failed to make clear connections between the physical situation and the given graph. A very common mistake candidates made was to think the question was about intensity and to therefore describe the decrease in peak height of the maxima on the graph. Another common mistake was to approach this as a Doppler question and to attempt to answer it based on the frequency difference of B.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates recognized that the wavelength was 26 cm, but the explanations were lacking the details about what information the graph was actually providing. Examiners were looking for a connection back to path difference, and not simply a description of peak-to-peak distance on the graph. Some candidates did not state a wavelength at all, and instead simply discussed the concept of wavelength or suggested that the wavelength was constant.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was a "show that" question that had enough information for backwards working. Examiners were looking for evidence of using the wavelength from (b) or information from the graph to determine wavelength followed by a correct substitution and an answer to more significant digits than the given result.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates were successful in setting up a Doppler calculation and determining the new frequency, although some missed the second step of finding the difference in frequencies.</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">Monochromatic coherent light is incident on two parallel slits of negligible width a distance <em>d</em> apart. A screen is placed a distance <em>D</em> from the slits. Point M is directly opposite the midpoint of the slits.</span></p>
<p><span style="background-color: #ffffff;"><img 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"></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">Initially the lower slit is covered and the intensity of light at M due to the upper slit alone is 22 W m<sup>-2</sup>. The lower slit is now uncovered.</span></span></p>
</div>

<div class="specification">
<p><span style="background-color: #ffffff;">The width of each slit is increased to 0.030 mm. <em>D</em>, <em>d</em> and λ remain the same.</span></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Deduce, in W m<sup>-2</sup>, the intensity at M.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">P is the first maximum of intensity on <strong>one</strong> side of M. The following data are available.</span></p>
<p><span style="background-color:#ffffff;"><em>d</em> = 0.12 mm </span></p>
<p><span style="background-color:#ffffff;"><em>D</em> = 1.5 m </span></p>
<p><span style="background-color:#ffffff;">Distance MP = 7.0 mm</span></p>
<p><span style="background-color:#ffffff;">Calculate, in nm, the wavelength λ of the light.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Suggest why, after this change, the intensity at P will be less than that at M.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">ci.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Show that, due to single slit diffraction, the intensity at a point on the screen a distance of 28 mm from M is zero.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">cii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">there is constructive interference at M<br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><em><strong>OR</strong></em><br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">the amplitude doubles at M ✔<br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">intensity is «proportional to» amplitude<sup>2</sup> ✔<br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">88 «<span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">W m</span><sup style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:11.6px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">−2</sup>» ✔</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">«<span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s = \frac{{\lambda D}}{d} \Rightarrow » \lambda&nbsp; = \frac{{sd}}{D}/\frac{{0.12 \times {{10}^{ - 3}} \times 7.0 \times {{10}^{ - 3}}}}{{1.5}}">
  <mi>s</mi>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mi>λ</mi>
      <mi>D</mi>
    </mrow>
    <mi>d</mi>
  </mfrac>
  <mo stretchy="false">⇒</mo>
  <mrow>
    <mo>»</mo>
  </mrow>
  <mi>λ</mi>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mi>s</mi>
      <mi>d</mi>
    </mrow>
    <mi>D</mi>
  </mfrac>
  <mrow>
    <mo>/</mo>
  </mrow>
  <mfrac>
    <mrow>
      <mn>0.12</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>3</mn>
          </mrow>
        </msup>
      </mrow>
      <mo>×</mo>
      <mn>7.0</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>3</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mn>1.5</mn>
    </mrow>
  </mfrac>
</math></span> &nbsp; &nbsp;✔</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda&nbsp; = 560«{\text{nm}}">
  <mi>λ</mi>
  <mo>=</mo>
  <mn>560</mn>
  <mrow>
    <mo>«</mo>
  </mrow>
  <mrow>
    <mtext>nm</mtext>
  </mrow>
</math></span>» &nbsp;<span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">&nbsp;</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">«the interference pattern will be modulated by»<br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">single slit diffraction ✔<br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">«envelope and so it will be less»</span></p>
<div class="question_part_label">ci.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><em><strong>ALTERNATIVE 1</strong></em><br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">the angular position of this point is&nbsp;<span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta&nbsp; = \frac{{28 \times {{10}^{ - 3}}}}{{1.5}} = 0.01867">
  <mi>θ</mi>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>28</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>3</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mn>1.5</mn>
    </mrow>
  </mfrac>
  <mo>=</mo>
  <mn>0.01867</mn>
</math></span>«rad»&nbsp; ✔</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">which coincides with the first minimum of the diffraction envelope</p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta&nbsp; = \frac{\lambda }{b} = \frac{{560 \times {{10}^{ - 9}}}}{{0.030 \times {{10}^{ - 3}}}} = 0.01867">
  <mi>θ</mi>
  <mo>=</mo>
  <mfrac>
    <mi>λ</mi>
    <mi>b</mi>
  </mfrac>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>560</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>9</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mn>0.030</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>3</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
  <mo>=</mo>
  <mn>0.01867</mn>
</math></span> «rad»&nbsp;<span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">«so intensity will be zero»</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">&nbsp;</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><em><strong>ALTERNATIVE 2</strong></em><br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">the first minimum of the diffraction envelope is at&nbsp;<span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta&nbsp; = \frac{\lambda }{b} = \frac{{560 \times {{10}^{ - 9}}}}{{0.030 \times {{10}^{ - 3}}}} = 0.01867">
  <mi>θ</mi>
  <mo>=</mo>
  <mfrac>
    <mi>λ</mi>
    <mi>b</mi>
  </mfrac>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>560</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>9</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mn>0.030</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>3</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
  <mo>=</mo>
  <mn>0.01867</mn>
</math></span>«rad» &nbsp;&nbsp;<span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">distance on screen is&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 1.50 \times 0.01867 = 28">
  <mi>y</mi>
  <mo>=</mo>
  <mn>1.50</mn>
  <mo>×</mo>
  <mn>0.01867</mn>
  <mo>=</mo>
  <mn>28</mn>
</math></span>«mm» &nbsp;<span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">«so intensity will be zero»</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">&nbsp;</p>
<div class="question_part_label">cii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This was generally well answered by those who attempted it but was the question that was most left blank. The most common mistake was the expected one of simply doubling the intensity.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was very well answered. As the question asks for the answer to be given in nm a bald answer of 560 was acceptable. Candidates could also gain credit for an answer of e.g. 5.6 x 10-7 m provided that the m was included.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many recognised the significance of the single slit diffraction envelope.</p>
<div class="question_part_label">ci.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Credit was often gained here for a calculation of an angle for alternative 2 in the markscheme but often the final substitution 1.50 was omitted to score the second mark. Both marks could be gained if the calculation was done in one step. Incorrect answers often included complicated calculations in an attempt to calculate an integer value.</p>
<div class="question_part_label">cii.</div>
</div>
<br><hr><br><div class="specification">
<p>A buoy, floating in a vertical tube, generates energy from the movement of water waves&nbsp;on the surface of the sea. When the buoy moves up, a cable turns a generator on the&nbsp;sea bed producing power. When the buoy moves down, the cable is wound in by a&nbsp;mechanism in the generator and no power is produced.</p>
<p style="text-align: center;"><img 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"></p>
<p>The motion of the buoy can be assumed to be simple harmonic.</p>
</div>

<div class="specification">
<p>Water can be used in other ways to generate energy.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline the conditions necessary for simple harmonic motion (SHM) to occur.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A wave of amplitude 4.3 m and wavelength 35 m, moves with a speed of&nbsp;3.4 m s<sup>–1</sup>. Calculate the maximum vertical speed of the buoy.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch a graph to show the variation with time of the generator output power.&nbsp;Label the time axis with a suitable scale.</p>
<p><img 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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline, with reference to energy changes, the operation of a pumped storage hydroelectric system.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The water in a particular pumped storage hydroelectric system falls a vertical&nbsp;distance of 270 m to the turbines. Calculate the speed at which water arrives at&nbsp;the turbines. Assume that there is no energy loss in the system.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The hydroelectric system has four 250 MW generators. Determine the maximum time for which the&nbsp;hydroelectric system can maintain full output when a mass of 1.5 x&nbsp;10<sup>10</sup> kg of water&nbsp;passes through the turbines.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Not all the stored energy can be retrieved because of energy losses in the system. Explain <strong>two</strong> such losses.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iv.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>force/acceleration proportional to displacement «from equilibrium position»</p>
<p>and directed towards equilibrium position/point<br><em><strong>OR</strong></em><br>and directed in opposite direction to the displacement from equilibrium position/point</p>
<p>&nbsp;</p>
<p><em>Do not award marks for stating the defining equation for SHM.</em><br><em>Award <strong>[1 max]</strong> for a ω–=<sup>2</sup>x with a and x defined.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>frequency of buoy movement&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{3.4}}{{35}}">
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>3.4</mn>
    </mrow>
    <mrow>
      <mn>35</mn>
    </mrow>
  </mfrac>
</math></span>&nbsp;<em><strong>or</strong></em> 0.097 «Hz»</p>
<p><em><strong>OR</strong></em></p>
<p>time period of buoy&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{35}}{{3.4}}">
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>35</mn>
    </mrow>
    <mrow>
      <mn>3.4</mn>
    </mrow>
  </mfrac>
</math></span> <em><strong>or</strong></em> 10.3 «s» <em><strong>or</strong></em> 10 «s»</p>
<p><em>v</em> =&nbsp;«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2\pi {x_0}}}{T}">
  <mfrac>
    <mrow>
      <mn>2</mn>
      <mi>π</mi>
      <mrow>
        <msub>
          <mi>x</mi>
          <mn>0</mn>
        </msub>
      </mrow>
    </mrow>
    <mi>T</mi>
  </mfrac>
</math></span>&nbsp;<em><strong>or&nbsp;</strong></em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi f{x_0}">
  <mn>2</mn>
  <mi>π</mi>
  <mi>f</mi>
  <mrow>
    <msub>
      <mi>x</mi>
      <mn>0</mn>
    </msub>
  </mrow>
</math></span>»&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\ = \frac{{2 \times \pi &nbsp;\times 4.3}}{{10.3}}">
  <mtext>&nbsp;</mtext>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>2</mn>
      <mo>×</mo>
      <mi>π</mi>
      <mo>×</mo>
      <mn>4.3</mn>
    </mrow>
    <mrow>
      <mn>10.3</mn>
    </mrow>
  </mfrac>
</math></span> <em><strong>or</strong></em>&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2 \times \pi &nbsp;\times 0.097 \times 4.3">
  <mn>2</mn>
  <mo>×</mo>
  <mi>π</mi>
  <mo>×</mo>
  <mn>0.097</mn>
  <mo>×</mo>
  <mn>4.3</mn>
</math></span></p>
<p>2.6 «m s<sup>–1</sup>»</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>peaks separated by gaps equal to width of each pulse «shape of peak&nbsp;roughly as shown»</p>
<p>one cycle taking 10 s shown on graph</p>
<p><img 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"></p>
<p><em>Judge by eye.</em><br><em>Do not accept cos<sub>2</sub> or sin<sub>2</sub> graph</em><br><em>At least two peaks needed.</em><br><em>Do not allow square waves or asymmetrical shapes.</em><br><em>Allow ECF from (b)(i) value of period if calculated.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>PE of water is converted to KE of moving water/turbine to electrical energy «in generator/turbine/dynamo»</p>
<p>idea of pumped storage, <em>ie:</em> pump water back during night/when energy cheap to buy/when energy not in demand/when there is a surplus of energy</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>specific energy available =&nbsp;«<em>gh</em> =» 9.81 x&nbsp;270 «= 2650J kg<sup>–1</sup>»</p>
<p><em><strong>OR</strong></em></p>
<p><em>mgh</em>&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{1}{2}">
  <mo>=</mo>
  <mfrac>
    <mn>1</mn>
    <mn>2</mn>
  </mfrac>
</math></span><em>mv</em><sup>2</sup></p>
<p><em><strong>OR</strong></em></p>
<p><em>v</em><sup>2</sup> = 2gh</p>
<p><em>v</em> =&nbsp;73 «ms<sup>–1</sup>»</p>
<p>&nbsp;</p>
<p><em>Do not allow 72 as round from 72.8</em></p>
<p>&nbsp;</p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>total energy =&nbsp;«<em>mgh</em> = 1.5 x 10<sup>10</sup>&nbsp;x 9.81 x 270=» 4.0 x 10<sup>13</sup> «J»</p>
<p><em><strong>OR</strong></em></p>
<p>total energy =&nbsp;«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}m{v^2} = \frac{1}{2} \times 1.5 \times {10^{10}} \times ">
  <mfrac>
    <mn>1</mn>
    <mn>2</mn>
  </mfrac>
  <mi>m</mi>
  <mrow>
    <msup>
      <mi>v</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>=</mo>
  <mfrac>
    <mn>1</mn>
    <mn>2</mn>
  </mfrac>
  <mo>×</mo>
  <mn>1.5</mn>
  <mo>×</mo>
  <mrow>
    <msup>
      <mn>10</mn>
      <mrow>
        <mn>10</mn>
      </mrow>
    </msup>
  </mrow>
  <mo>×</mo>
</math></span> (answer (c)(ii))<sup>2</sup> =» 4.0 x 10<sup>13</sup>&nbsp;«J»</p>
<p>time =&nbsp;«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4.0 \times {{10}^{13}}}}{{4 \times 2.5 \times {{10}^8}}}">
  <mfrac>
    <mrow>
      <mn>4.0</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mn>13</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mn>4</mn>
      <mo>×</mo>
      <mn>2.5</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mn>8</mn>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
</math></span>» 11.1h&nbsp;<em><strong>or</strong> </em>4.0 x 10<sup>4</sup> s</p>
<p>&nbsp;</p>
<p><em>Use of 3.97 x 10<sup>13</sup>&nbsp;«J» gives 11 h.</em></p>
<p><em>For MP2 the unit <strong>must</strong> be present.</em></p>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>friction/resistive losses in pipe/fluid resistance/turbulence/turbine or generator «bearings»<br><em><strong>OR</strong></em><br>sound energy losses from turbine/water in pipe </p>
<p>thermal energy/heat losses in wires/components<br><br>water requires kinetic energy to leave system so not all can be transferred</p>
<p> </p>
<p><em>Must see “seat of friction” to award the mark.</em></p>
<p><em>Do not allow “friction” bald.</em></p>
<div class="question_part_label">c.iv.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iv.</div>
</div>
<br><hr><br><div class="specification">
<p>An experiment to investigate simple harmonic motion consists of a mass oscillating at the&nbsp;end of a vertical spring.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAR8AAAFqCAYAAAAjuF4/AAAgAElEQVR4nO3de0CUZcI28GvZ8k0iV5EvyFQGOTUgYiQq6re6SSooHrAXjyXlWUtRTDcFDytaHtFMobLCFY9bCh1085B0cjbRkQmUZCBAHcUWp8JpprWVef+AZxwQFHVm7ge4fn8JPPM89yBc3Of7D2az2QwiIgdzEl0AImqeGD5EJATDh4iEeEB0AZojH4WX6CIQ2UxhSfE9vY41HyISguFDREIwfIhICIYPEQnB8CEiIRg+RCQEw4eIhGD4EJEQDB8iEoLhQ0RCMHyISAiGDxEJwfAhIiEYPkQkBMOHiIRg+BCREAwfIhKC4UNEQjB8iEiIP/DcLpKL1JRURA2NwuOPPy66KOQADB+SDb1ej5nTp2Pt+vX3HUBardby77Nnztzx+oDAQABA27Zt4erqel/PpoZh+JCsqFQqLHr1VcyOi8OAgQPRsmXLeq/V6/W4cOECSoqLUVBQgF9++QW7d+y0fH30uLGWfyuVSri4uNR5n+zsbADATz/9hM8OHLS8VqlUwv+JJ9CtWzdbvDWqheFDsqPT6bByxQror17F6DFjLCGk1+tx7tw5fP3VVzh44ADOl5RiYGQEgoK64LHHPBAQGAhnZ+f7rjVJoZaXm4vTp09Dd/GiTWpjVBPDh2RLpVIhed16qE+eRAfPjrhQeh7PjopBWFgYAgID4evr67ByHPj0UyxPSnLI85oLHhpIsmQymfDjlSsoL/83+g94Bm3atIHZDHywZy+uXbsGg8EAo9GIDh062LWPRiqHyWSy2zOaK9Z8SHY0Gg3mzJ6NmFGjETMqpka4aDQa5OXmIj8//5b+nfbtO+CxxzzwqLs73NzcAOCuakcmkwkXL16E0WhESXExsrOzsXvHToweNxbTZ8xgs8vGGD4kKyqVCunbt2PhokUN+mXX6XQoLy+v0elcVFiI7G9P1Hl9R4UnevXuDaBmB3PtryuVSnTy9oa/vz9Hv+yE4UOyodVqsSE5GWvXrbvtKNfd0Ov1uHr16h2va9++vc2eSQ3D8CHZ2JGejuiRIxkCzQSXV5BseCoUDJ5mhOFDsmE9K5maPoYPyYZrmzZQqVSii0EOwnk+JBsDBg7Ei7Gx+PXXXxEeHn5P95BqT6WlpfjVYAAAyyhYff70pz/Bz88PACzD9I6awNicscOZZEWn02He3Lnw9vG57dwaaanFD0VFyM/Px/FvvsH5ktIaQ+mhoaGW663n/liT5vQAgMFgQH5+vmWofmBkBHr06IEhUVEcbrcDhg/Jjslkwra0bVi7ahWmzpiOAQMHws/PDzk5OdDkaLB3z26cLym1LP7s5O1t89qKyWRCQUEBsk+cwOsrVmL7rp0ICwuz2f2J4UMyptfrsfnNzdj23nsAgE4+3hgSFYWn+/dH586dHVqO1atW4/VVrzvsmc0Bw4dkSavVYltaGooKCxE9ciQeePBBnDp50rKkYmBkBHr16mWXWo81jUaDf+zdC3d3d7w8a5ZdntFcMXxIdnakp+OTjz/GrLi4W5o6UnNIWnsl9fUAQGiP7vD28bGs8QJubhImsd5yQ1rLJZH6f6S+n907diK0R3eMHjMGw4YPt+dbbpYYPiQrqSmpAIAJsRMaPOFQChFphOvy5TJcvHgBAG67zsvawMgItGnTxjLypfDysvuK+eaO4UOyoVKpoMnRYNr0aaKLQg7ASYYkGz8UFTF4mhGGD8nG2bNnRReBHIjhQ7LRunVr0UUgB2L4kGw8GRJi6XCmpo8dziQrM2fMQFBQl7sa7QKqlmUYjUbLGV3ScTgAagzH18V6SYY0TB8QGMgNxuyM4UOyYjKZ8OamTTh44ABWvPZanUsadDod8vPzUagtRG7udzXO2rJeJGo9x6e+wwCt5/pI83wuXy6z3Hfs+PGIGBzJpRV2wPAhWZIODwSAiZMmoaOnJ87knamxris0NNSu83FMJhNOnTqFzZs2YUhUFMaNH2/zZzRnDB+SrZ9++glb33kH772zFb///jv8nngC4c+EI2roUIdueWEymZCYkIC169Y57JnNAffzIVnKzMjAxg0bEDNqND468CmcnZ1xMjsbhw4dQsQzAwDAclqpj68PPD09bX7OularxYlvv8W7W7diYUKCze5LVVjzIVkxmUyYFx8PhUKBiZMm3baf5uyZM8jOzr5lCUXtpRLWFF5ecHZ2tnwsdVBLsrOzLUfqhPbojr79/oL+4f25uZgdMHxINkwmE1YkJWHwkCH31MErjXjdzS6GEqVSCRcXFzzs4gJPT0+OdDkAw4dkIzUlFWG9whAcHCy6KOQAnGRIsvHIIy4MnmaE4UOyceXKFdFFIAdi+JBsODs/DJPJJLoY5CDs8yHZ0Gg0ePutt2x6VjtwsyO6Pta7G5LjMHxIVlJTUpGb+x3i5sxp0PB27V0MpTVd0l7PEmmL1dqkYfXa10mzp9kHZT8MH5KdzIwMxMfNwbwFCxAzKqbGXB9pXddptRrqU6eQ/e2JGoEhDZUDuOu5OVKQlZeX44eiIhw/fhzXrl1Dr16973qhK90Zw4dkSa/XY/26ddi9Yyf+f7++8FJ4IS8vF+qTpyzruhyx8lyv12Pvnr34Sa/Hq4sW2u05zRGXV5Asubq6YkJsLH777TccPXwEOerTuFZRgYGREQ4LHqkc/cP7IzUlxa7PaY5Y8yHZkWo9RYWFmBUXh65du6Jly5bQaDTIy83F8ePHLf00oT26I+Spp+Dn52c5Evl+Q8l6+cahQ4eQf/Ys3nrnHS6xsDGGD8mKRqPB6ytXYuLkyQgPD6/3OuuAkI7Kqb1pmPUmYRLrM72AmpuOWXc+S4tWg7sGcy8fO2H4kGzodDqkbNmC6TNm3NfQt/XQuvU6r9uRFpxy2N1xGD4kG6kpqbeMblHTxRnOJBv//e/vDJ5mhOFDsnH9+nXRRSAHYviQbDg7PwydTie6GOQg7PMh2dDpdJg3dy7Wrl9/352+d9PpLA3RA+AmYg7E8CFZkU6tWJiQcNuhdqBqPtCFCxdQUlxs2bHQek3X6HFjLf+ua0tVAJZhegA1tmOVZlF3DgqCt7e3Ld4a1cLwaVQqUZG1DH1iixB/eCsm+D4kukB2odVqsbh6w3brSYZ6vR5qtRqn1WocPHAA50tKLfNxpIP+bDFUrtPpcP78eWhyNCgs1EJ38aJNamNUE8OHZMlkMuHQZ58heX0yjMZf0bp1a/xQWIRnR8UgLCwMAYGBDptxrFKpsGf3bmzYuNEhz2suuLaLZOvy5TI4Of0BQUFd8LDLw/ihsAgf7NmLBx6o+rE1Go12OzBQYjKZ8OOVK3jkkUfs9ozmiqNddlEJg/YwNkwKg4/CCz6KQAxO2Al1WfVQckUWEgP6IjHjS2QmDKu6JmAyNhzVwtItWpGFxIAwTFmzAlMCvOCj6IvErB9RkbUEXRTjsU37G4ByZCX0RZeEfTh5dFP1dV7oMikVJ8ush62vo0y9E4kRgdVf34TDGWsxwnIfeVGpVBgcEQEA+GDfPrz7/nt4Y9Mm5OafxYeZGVAqlTh06BBGDhuO7iFP4el+/ZCwaBF2pKcjMyMDGo0GWq32nkbOtFotNBoNMjMykLBoEYKUASgoKMDCRYts/TabPdZ87KHiS6wathhXV+5BwdaOcKq8hKxl0xEz9ToO7o9FVWPhPHbFrcMf01JQkOQB47mdmDviecxfuQdvDu9Y/VehDJ9/Dmz9/BzedvkZZXAFTt76OGP6Grz96Hr8La8YbxvPYFvcJIye+lDVs5wqYVC/hYnjv8OgbUdREPpo9bMSkYveGO7I70sDSJuJbd+x45Y+lpYtWyI4OBjBwcGWo4u1Wi3Ky8vx45Urlk7njRs21FjjZc26ExpAvevBlEolBg8Zgrnx8Zz4aCcMH5urRIX6GDKN3ogPfLQqRJzaod+yTBTWuM4Z/rMTMK9fOzgBcPGPwdKVpzDo/c9RNFQKKMD5qd4I8WgB4FF4oBIVdT0yeCpeeSkMHk4AXJQYMX4A1sUewfGi0fD1NeDkvo/QYv6bmBnqUf2sZ/HK/H/i86X2+y7cC41GAwDYvGVLg1/j6+t7276fO22hOiE2FgCH2EVg+NicE1p1G4IXlbFYPisJmNoHQT2frg4Qa24IedILLpaPW8AjMBjemurQcAcAZ3j7PGZ1zT2oyMPRfdfReUtbqzb2Q/DuHY4gHLmfO9vcoc8+w0svv2zTe3KESr7Y52MPLqGY9f52bJjcFt8snI6Ynv7wiUjAtiyrPh0HqbxSgrz6//DLisdjj7H20Yyw5mMnTh4hGBIdgiHRc1BZpsbHu1KQGLsMOLwVE9wdWA53BTo73/k6iY/Cy36FaYBliYvr/HxhSbGDS0L2xvBxACePEAybOA4n31mCQp0BcAeAcuSVXEUl3Kqrn7+h6JsjyA0Ox2rvh2CzKlKrzugf3QIbazzrOsrOaFBUx+Uif8lTU1LRP7w/dwxsJhg+NlcJg3ozRo3/DoO2La/u5L2OMvU3UCMEU/xaVV9nRO7qtdgcuBwzQx+F8dwHWLPahJfSh8PXpo1hV3SLHorr462ftRdLF2bAiN53frkDxYyKwczp0zErLu6edw/UarUAgLNnzlg+J42C1cd66YW0qRgD0P4YPjbnBJeQCdiwZR/+vrg//PKrOlycw+diQ+bLeLpdC1QNWTnDP7orbrw1An7/WwYox2Fp+maMDWlth/JMxbvpH2DzoqryOIfPwuLJ4fjXRnmdDurq6oq169fjuXHjEBEZiYmTJtU7zC0tgfihqAj5+fmWIXPrrVNDQ0MBoMb+zrVJw/RA1aTG7Oxsy71GjxuL7j164JlnnmFflB1weYUIFVlI7DkTefP34cNYfwG9/tVrxGYAb/xrCfq1kte4g8lkwpubNuGtLSmYt2AB+of3R/v27ZGTk4Ovv/rKsq5r9LixUCqV6OTtDTc3N5vWVvR6Pc6dO4czeXnYuWMHVrz2GvdytjUzOd4vx8wJygDz8Pe/N9+w97NufG9OG/qkOXLxEfPl6ofduHzc/MbEP5sj158wX7P38+9DQUGBecH8+WZvT4XZ21Nhjhg4yJyyZYu5oKDAoeW4evWq+eWXXnLoM5sDNruaOidfjFy7HtiWjD6dJlV9zjkcL61MxrtDQ+5vDpEdWa9sX5a0HM4PP4wjhw9j7arVWLtqtWXLC4WXF9zc3Ow2n0ej0eAfe/fiyZAQu9y/OWOzi2TFZDJhW9o2fJF1rM6OZ5PJhIKCAuTl5iI/P7/G/j0DIyPQpk0bKJVKuLi41Dg6WVK7aVZ7BvTZM2dgMBgs9w7t0f2Ox/jQvWH4kKzMnDEDvXr1QvTIkQ3u5NXr9bh69aplhMt6dMs6nG5HCi5p5Evh5WX3FfPNHcOHZCMzIwOPuruzY7eZkNcwBzVrly+XMXiaEYYPyYbTH/nj2Jzwf5tk45effxZdBHIghg/Jhp+fH1QqlehiNHqZGRmWZSZyxg5nkg2TyYR58fF3PdoF3Bwyr2vEy/pInLqE9ugObx8fAIBSqYS7hwc8PT0b5fouvV6P7iFPYWBkxF1tyiYCw4dkxWQyYUVSEooKC+tdYKrT6ZCfn49CbSFyc7/DZwcOAqjaItV6kWhAYKDlNW3btq1z2FwapgdQYztW9alTyP72BCZNnYKRzz7baIJozerVeGtLCgAgdes7sp6fxPAhWTpy5AhWJiXB3d0do8eMgWvbtjiTdwZ79+y2rOuSZjjbaz6OXq/H2bNnsXnTJoweMwbDhsttx+uatFotIp4ZYPm4o8ITnx48KNtFsQwfkq1Lly7hva1bsWN7On7//Xf4PfEEhg4b5vA9f0wmE2a9/DLe2brVYc+8FzNnzLDUAiXLkpZbNtuXG4YPyY50YGB83BzMW7AAUUOjAABZx47h+PHjNZpZ1n00tt4EXqvV4sS33+LdrVuRvHEjgoODbXZvWzty5AimTZpc59dOqE/JcqY2w4dkRafTYeWKFQgK6oKYUTF1/tJI67tKiouRnZ19S4dy7aUS1qz7gYCam45Ja7p++uknfHbgIEJ7dMeQqChEREbK8pfX2prVq2ssKbE+Iig0NFSWTUaGD8mGyWTCi7Gx+OvChfdUy5CGl0tLS/GroWof2uzs7Aa9tvZi1MZ8lI6PwqtR7HnN8CHZSE1JRdTQKB53c58aS/hwkiHJxkMP/Q+Dpxlh+JBsNNZmDt0bhg/JRm5urugikAOxz4dkQ6VSQZOjwbTp02x63zud117f7OfGqrH0+XAPZ5KNsLAwaHI0mDljBpYnJTUoEEwmEy5evGgZ4ZJGt6TjbyTWR+pYq33dwMgIKBQK+Pn5ISAwsNEsq2iMWPMh2dmRno4lCYmYt2DBLXN9pHVdp9Vqy/oraWFoaGhojX2b7zY4pHVepaWlKNQW4ousY3iwRQuMHDkSAwYObDR9Uo2l5sPwIVnSarXYlpaG3Tt2Ysz4cXjwgQeRl5cL9clTlnVdAYGBdp+Pc+nSJXyU+RGMRiPmxs+123NsqbGED5tdJEu+vr4YPGQIzpeW4pOPPgYAXKuoqBE8jmgStWvXDv3D+yNF5ttTNEYMH5IdaYmF/urVGttqaDQa5OXm4tChQ4iPmwOgZh+NdM76/daGpH6ks2fO4NChQ9BfvYq169fb5L3RTWx2kayoVCosevXVOx5PbB0Qly+X4eLFC7cck2O9SRiAOtd6Sa+VSPcYGBmBoKAuCOsVJusFpXVpLM0uhg/JhlarxYbk5AaPdN3uPhLrhaO386i7O9zc3ODs7NzoZ1k3lvBhs4tkI2P/fqxdt+6+O5Ct+4I4VC5fnOFMsuHj69tohrPp/jF8SDb+/eOPootADsTwIdk4f/48TCaT6GKQg7DPh2Tjf2NiMC8+3ib9Ptadztabi9VF6mwG0Kg3EWtsONpFstLQoXagajnEhQsXUFJcbDmny3q43Xor0bqG2YG6z/eS1oGFhoaic1AQvL29bfTuHKOxjHYxfEh2NBoN5syeDXd39xqTDPV6PdRqNU6r1Th44IDlCJ327Tvgscc8EBAYaJOhcp1Oh/Pnz0OTUzWpsXWb1pg+Y0ajGYJn+BDdB+kEi+T1yTAaf0Xr1q3xQ2ERRo8bi35/+YvDThSVyqFSqfD6qlV2f54tNJbwYZ8PyZLJZKqafXz+PCKjhgAAfigssjSrQkNDATiuj+bhh13s/ozmhjUfkh3ptNKYUaNrbKlhMpmQk5MDTY6mxjHJUh+NdAKFdDzOvWwSptVqYTQaLcfy7N6xE/MWLMCE2AmNpiO6sdR8GD4kK6kpqbh48QLmxsc3KDi0Wu0tG4nVXuMlqWtDsfo2HVMqlejk7Y2uXbs2mtCRMHyI7tKRI0dQqC206Taq1kPut9OUtlJtLOHDPh+SDVsHD8C1XXLGGc4kG4+3bxxD2WQbDB+SjZJi+TcVyHYYPiQbDz7YAjqdTnQxyEHY50OyETU0CvPmzsXfkpLuua9G6mC2Xs9Ve7fC2qQhegA2myVNd8bRLpIVnU6H58aNu2WOT13XnT9/Hj8UFSE/P98yZG49nC5NRJRI83+sWe90WHt92OhxY9GzZ0/0Dw9vVMPtjWW0i+FDsqPX67F+3TrLBL+ooVFwdXVFTk4Ovv7qqxrruqT5OG5ubjYd2dLr9Th37hwOHjiAr7/6CskbNzaavZwZPkT3SavVYu2aNTh66DAAwO+JJzB02FD0Dw936BC6VqtFypYtWJ+c7LBn3g+GD9F90Gg0eH3lSgBAzOjRMP76K44fP25ZUiGd36Xw8kKHDh3sNkFQpVIhfft29OrVC+PGj7fLM2yN4UN0D0wmE97ctAnqU6dqbKchkZpDUl+P9VKKgZERaNOmjaWvx3qTMAB1diTrdDoYjUYAsKzpMhgMlnsPjIzA+Oeeu+PeQnLC8CG6SyaTCfPi4zFgwAAMGz68wa+TAkTqPJbWeAH1r/OqTQouadMxe9eo7InhQ3SXdqSno5O3d6OqZchRYwkfTjIkWWHwNB8MH5INdw8P0UUgB2L4kGycVqtFF4EciOFDsvHII62gUqlEF4MchOFDsjEhdgLSt2/HjvR0Hh7YDDB8SDZatmyJtevW4dKlS3gxNpa1oCaOQ+0kS1qtFtvS0lBUWIiJkycjJCSkUc65EaGxDLUzfEjWtFotjh45ir17dkMZEIAR0dFQKpXc8uI2GD5ENqbRaKA6rsIXWcdw5coVy5HGCi8vuLm5MZCqMXyI6uCj8BJdBJuS4y95Ywkf7mRIDvf2+2mii2ATU16IFV2ERo2jXUQkBMOHiIRg+BCREAwfIhKC4UNEQjB8iEgIho/DlCMroS+6/DUNn29PwGCFF3wUgRickAFtxSWoLZ8Lw5Q3VCirtHppZRnUGcmYEuAFH+ma5MPQGqSLKmHQHsaGSWHVXw/E4ISdUJddv3kPgxafJ09GF0X1PSISkK4ug/VjiByJ4eNgxt1vYfeNMdhTUoyC4yvguW8OIrpMx/5HnsOekiLkfDYTSP0rNn9ZXv2Kn6HeOBOxn/w/xJ8oQmFJEXIOL4D7oQWY/4G2KjwqvsSqYYtRMGQPCkqKUfjDYbzyxz2ImboT2koAKEfW65MQVzAY//yhGIUl5/D1gpbYFT0P27W/CfteUPPG8HG04Kl45flAuABwatcHMdEdgeAReH6oP1zgBBffUPT2LUfmkTxUAEBFDva/U45h4wfB38UJgBNcfPug/1OPIHe/CkWVlahQH0Om0Rs9Ah+t+g91aod+yzJRmBkLXycAFXk4uq8c3j2U8HACgBbw6LcIn5akY4LvQ8K+FdS8cYazDDgHKeBe35+BVv2w/OwXqCxT45OMr3EDlfj55DYsTz8PBAOAE1p1G4IXlbFYPisJmNoHQT2fRohHC6t7dMWIyU9g19L5WIIJ6NGlFyJDPPiXh4Tiz5/sVeBc2nR07fkcUk7qATihbfRyvD2+481LXEIx6/3t2DC5Lb5ZOB0xPf3hE5GAbVlaGAAArREyezP2bhqLtl+vQVx0GPwUw5CYlmXVb0TkWKz5yFyldh/+uvRHvLjvG8SFtK7+bDmy9tW8zskjBEOiQzAkeg4qy9T4eFcKEmOXAYe3VjWtnDwQEjUKIVGjEFdZBvVHu5C6cCbmYx8+jPW3/BVyxMLPe1kT1VTWg9FNDB9Zq4RBV4wi586Y7dPK6tNXUZpbXu+rnDxCMGziOJx8ZwkKdQagdr+OkwdChj+HsSczMKvwMgzwh3R3e6+G9lF4MUgIAJtdMucEF78n0QeHsPfzi1UjWwYtPt+4Fus0xuprKmFQb8LggMnYlC0NnV9HmfobqBGCbn6tAEM2NkT0rTGEX1mmQdYpoE+3TnAR8dao2WP4yJxTu0gs3jYB/13YF34KL/h0X43vvKbgH+8+D2dtMXQGwCVkAjZs6Y0fF/evukbhjwHprRCfuQzD2rUAXJ7CpDeWofePr6NPp6p5Pn5P70breVuxenhH/hCQENxMjByqKTW7prwQK8tNuxrLZmL8o0dEQjB8iEgIhg8RCcHwISIhGD5EJATDh4iEYPgQkRCc50P3rKkdAOgojljCwnk+RET1YPgQkRAMHyISguFDREIwfIhICIYPEQnB8CEiIRg+RCQEw4eIhGD4EJEQXF5B1ASMGTUK2d+eqPNr8xYswLTp0xxcojtj+BA1ARqNBiOHDb/l8x0Vnvj04EG0bNlSQKluj80uoiYgODgYo8eNveXzs+PiZBk8AGs+RE2GXq9H95CnLB+H9uiOXXv2CCzR7bHmQ9REuLq6YlnScsvHf0tKEliaO2P4EDUh0SNHoqPCE6PHjYWvr6/o4twWm11ETYxKpYK/vz9cXV1FF+W2GD5EJASbXUQkBMOHiIRg+BCREAwfIhKC4UNEQjB8iEgIhg8RCcHwISIhGD5EJATDh4iEYPgQkRAMHyISguFDREIwfIhICIYPEQnB8CEiIRg+RCQEw4eIhGD4EJEQDB8iEoLhQ0RCMHyISAiGDxEJwfAhIiEYPkQkBMOHiIRg+BCREAwfIhKC4UNEQjB8iEgIhg8RCcHwISIhGD5EJATDh4iEYPgQkRAMHyISguFDREIwfIhICIYPEQnB8CEiIRg+RCQEw4eIhGD4EJEQDB8iEoLhQ0RCMHyISAiGDxEJwfAhIiEYPkQkBMOHiIRg+BCREAwfIhKC4UNEQjB8iEgIhg8RCcHwISIhGD5EJATDh4iEYPgQkRAMHyISguFDREIwfIhICIYPEQnB8CEiIRg+RCQEw4eIhGD4EJEQDB8iEoLhQ0RCMHyISAiGDxEJwfAhIiEYPkQkBMOHiIRg+BCREAwfIhKC4UNEQjB8iEgIhg8RCcHwISIhGD5EJATDh4iEYPgQkRAMHyISguFDREIwfIhICIYPEQnB8CEiIRg+RCQEw4eIhGD4EJEQDB8iEoLhQ0RCMHyISAiGDxEJwfAhIiEYPkQkBMOHiIRg+BCREAwfIhKC4UNEQjB8iEgIhg8RCcHwISIhGD5EJATDh4iEYPgQkRAMHyISguFDREIwfIhICIYPEQnB8CEiIRg+RCQEw4eIhGD4EJEQDB8iEoLhQ0RCMHyISAiGDxEJwfAhIiEYPkQkBMOHiIRg+BCREAwfIhKC4UNEQjB8yGZUKpXoIsiKRqOByWQSXQzZYviQzaRv347UlFTRxZAFlUqFkcOGo6CgQHRRZIvhQzazdt065OZ+1+wDSKVS4bkxY7F9104EBweLLo5sMXzIZlq2bNnsA8g6eMLCwkQXR9YYPmRTzTmAGDx3h+FDNtccA4jBc/cYPmQXzSmAGDz3huFDdtMcAojBc+8YPmRXTTmAGDz3h+FDdtcUA4jBc/8YPuQQTSmAGDy2wfAhh2kKAcTgsR2GDzlUYw4gBo9t/cFsNptFF4KaH5PJhHnx8XBzc0PBuXPI/vaE6CLVq6PCE2G9emHPzl0MHhti+JAweXl5iI+bgxEjR2La9Gmii1MvlUqFv74yH3379cPfkpaLLk6TwWYXCWi+iMYAAAeVSURBVFNUWIjwAc/IOngAICwsDIlLl6DSXCm6KE0Kw4eE8vPzE12EBvH09BRdhCaH4UNEQjB8iEgIhg8RCdF0wqeyDOqdH0NdUd0pWJGFxIBAjEg7B3YTEsnPA6ILYBuVqPgyBbFJwBtDBld9qlU/LD97RmyxiKheTafmQ0SNigPDpxIVWUvQJeAVbDuajsSIQPgovOATsQSZ2nKUqXdaPtdlUipOll23eu11lKkzsGFSWNVrFMOQmJYFraESwG/Qpj2PkNi/w2j8OyZ1CapqatXR7KosUyMzeTK6KLzgowjE4IQ0ZGkrapUvAZnZ/7z5rIDJ2JRddvumm0GLzy339YJPRALS1davqYRBe7hm+bdno6zy5tcb9uwKaI9uwpQAr3rug6rmZ0byzWsiErAtSwuD5RZZSAwIw5Q1K6qv6YvErPK7/t8kum9mh7lh/uXYYnOQp8IcNHG7+ftrN8zmG6XmjGk9zd6eAebIRfvNBddumM3X8sxpE3uagxYdM/9S/bprp94wR3oONS85pjPfMJtvXjNtv1l3w+reysXmY7/cqHrcL8fMCcoA8/D3v69+zQlz8qAnzZGLj5gv3zCbzeZfzN+/P80cpIwzZ+j+U6t8Kebsy/+5eY3nOHNagame9/Vv87FFf7Yqy3/Ml48lmSOtXnNDt988XTnUnLD/e/M1S/n/bI5cf6Lq4wY9W3qPUnnN5huXj5iXDHry5ns0/2Q+tT7a7D0oyXzsctV7uvb9dvNkZU/z9P2lVdf8csycoFTcvObaFfPlazds9H98dzL27zdn7N8v5Nl3q6CgwLxo4ULRxWhSBDS7eiN+wbPwd3ECnNrjL6MGwBlPImbCIPi6OAEu3ujVxxvGfceqOo8rtfhw2fvA7ATM69euqqrmEojn/rYAfb5IRsqXDfmr/Ru0H2zEm3gBy1/5CzycAKAV/J9/Fcv7/guJW46jwnJtb8QviEU3jxZV10SPwjDn08j4prTu2k9FHo7uK4d3D2X1fVvAo98ifFqSjgm+DwEox5dbkvF19By8MtwfLlL5F7yAFhs34kPtb7W+N/U9Ww/1kSwYfYMR4NECAODk0R9LD6qxP9YfTgAqtRlYvhF4acVM9PNoAcAJLv4xWLqyJ75e+C6+rLj5Dpyf6o0QjxaAy6PwcGHrmxxPHj91zt7wdG9R99cMl1GofQQhT3pV/eJWc/JQoofvNeSVXG3AaJYBusILcH4qCD7Wv2hOjyKghzeMuSW4cq9DYq26YsTkJ5C7dD6WpO3DJ+paTTQpnHweq1l+dwU63y7UbuGKbtHPwl+zBnGL30Pmx+qazS1UwqArRpFzZ3T1aWX1+RbwCAyGt7EIpVekpqzzLeUhcjR5hM9tVF4pQZ6xvq/+B0WFl2/2Z9R7k6sozb1NDUlbDJ3hXtOnNUJmb8beTWPR9us1iIsOg1+NPikAMCJ36SD4SX1CCi/4dHkBu+p9X3VxgkvIVLy7bx0mtVUh8eWR6NPJut/qOq6UFKH+W15Aoe6O3ykih5H9UHtVDaG+r/6P5S/4bX+tnNrCM8it/q/7euHx+2l6OHkgJGoUQqJGIa6yDOqPdiF14UzMxz58GA0AHTEm7UMs71dfGRoafC3gETIII0IGYcSc6yhTH8DuLaswaR5wcP/zcFd4o95vFTrA5/E713V8FF4NLIvtxMfNueM1hSXFDigJOZLswwcuj8HH9xr2ni6GoZ+bpalQWZaPb7WPoLOibQOqby543KcDjHtyUWj4M0KkoKn8EWe/LYJz0CS426oO6OSBkOHPYezJDMwqvAxDq87oHw3MOpKHV/r1g6VBVJGFxJ5LgC0fYnk/13t4UAt4hAzFi+NP470ZxdAZAO/HveBt/Bg5hRXoF9K6+rrrKDujQdHtmrZWHPlLnpmRAQAYNny4w55J8iH7ZhecfDFyyQvAxiSszbpUVUcwnMH2xavwdd85mP5nq9qEsQilV4wwGH6rdZOH4PvsbLyE95G45lh1X0kFzv39NSR+0RPLZ/RCK9wjQzY2RPTFlDdUlj6YyjINsk4Bfbp1gkt1X02H9GSsyThXVUMznEPm6mRk1i7/bf0MdfLImtMQKsugPpYD9H0Sfi5OcPIdjsTZwJuLNiOr7DqAShjO7cXShf9Cn5UT8edW8v/vpuajEfw0Sn0dL6B1+siqfpPOC1HY5zV8uGYo2jlVXdOq21gsH38Ny5/pgec+qKMT1yUUs97fiimtd2NAJy/4KMIwt7AH3shchmHt7lwjqJfLU5j0xjL0/vF19OlU1Z/j9/RutJ63FauHd4QTnOASMhN7Dr+Etp/EoqvCCz6dY/Fp25esyt8QrREy+XW80ecilvT0r+o36jQSO1tb36e6/2mqM3Y+7Q8fhTe6xn2P3lv+Xl0WIvngToYkTGNqdmm1WmxLS0PSihWii9Jk8I8hEQnB8CEiIRg+RCQEw4eIhGD4EJEQDB8iEoLhQ0RCMHyISAiGDwl16NAhmEwm0cW4o9LSUtFFaHLkv7CUmqxuoaGWFe1xc+68sl2U0tJSTJs0Gct4TrtNcXkFCaXRaPCPvXtFF+OOQkNDMWDgQLRs2VJ0UZoMhg8RCfF/0Hw9hM2qHPcAAAAASUVORK5CYII="></p>
<p>The mass oscillates vertically above a motion sensor that measures the speed of the mass.&nbsp;Test 1 is carried out with a 1.0&thinsp;kg mass and spring of spring constant <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>k</mi><mn>1</mn></msub></math>. Test 2 is a repeat of&nbsp;the experiment with a 4.0&thinsp;kg mass and spring of spring constant <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>k</mi><mn>2</mn></msub></math>.&nbsp;</p>
<p>The variation with time of the vertical speed of the masses, for one cycle of the oscillation,&nbsp;is shown for each test.<br><br></p>
<p>&nbsp;<img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the frequency of the oscillation for both tests.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>k</mi><mn>1</mn></msub><msub><mi>k</mi><mn>2</mn></msub></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the amplitude of oscillation for test 1.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In test 2, the maximum elastic potential energy <em>E</em><sub>p</sub> stored in the spring is 44 J.</p>
<p>When <em>t</em> = 0 the value of <em>E</em><sub>p</sub> for test 2 is zero.</p>
<p>Sketch, on the axes, the variation with time of <em>E</em><sub>p</sub> for test 2.</p>
<p style="text-align:center;"><img 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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The motion sensor operates by detecting the sound waves reflected from the base of the mass. The sensor compares the frequency detected with the frequency emitted when the signal returns.</p>
<p>The sound frequency emitted by the sensor is 35 kHz. The speed of sound is 340 m s<sup>−1</sup>.</p>
<p>Determine the maximum frequency change detected by the sensor for test 2.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>1.3 «Hz» ✓</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>∝</mo><mi>m</mi></math>  <em><strong>OR </strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>m</mi><mn>1</mn></msub><msub><mi>k</mi><mn>1</mn></msub></mfrac><mo>=</mo><mfrac><msub><mi>m</mi><mn>2</mn></msub><msub><mi>k</mi><mn>2</mn></msub></mfrac></math> ✓</p>
<p>0.25  <em><strong>OR  <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>4</mn></mfrac></math> </strong></em>✓</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>v</em><sub>max</sub> = 4.8 «m s<sup>−1</sup>» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>0</mn></msub><mo>=</mo></math>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>v</mi><mi>ω</mi></mfrac><mo>=</mo><mfrac><mrow><mi>v</mi><mi>T</mi></mrow><mrow><mn>2</mn><mi>π</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn><mo>.</mo><mn>8</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>80</mn></mrow><mrow><mn>2</mn><mi>π</mi></mrow></mfrac></math>» = 0.61 «m» ✓</p>
<p> </p>
<p><em>Allow a range of 4.7 to 4.9 for <strong>MP1</strong></em></p>
<p><em>Allow a range of 0.58 to 0.62 for <strong>MP2</strong></em></p>
<p><em>Allow <strong>ECF</strong> from <strong>(a)(i)</strong></em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong>.</em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>all energy shown positive ✓</p>
<p>curve starting and finishing at <em>E</em> = 0 with two peaks with at least one at 44 J<br><em><strong>OR</strong></em><br>curve starting and finishing at <em>E</em> = 0 with one peak at 44 J ✓</p>
<p> </p>
<p><em>Do not accept straight lines or discontinuous curves for <strong>MP2</strong></em></p>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>read off of 9.4 «m s<sup>−1</sup>» ✓</p>
<p>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mo>=</mo><mi>f</mi><mfenced><mfrac><mi>v</mi><mrow><mi>v</mi><mo>±</mo><msub><mi>u</mi><mi>s</mi></msub></mrow></mfrac></mfenced></math>  <em><strong>OR  <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mo>=</mo><mi>f</mi><mfenced><mfrac><mrow><mi>v</mi><mo>±</mo><msub><mi>u</mi><mi>o</mi></msub></mrow><mi>v</mi></mfrac></mfenced></math> </strong></em>✓</p>
<p><em>f</em> = 36 «kHz» <em><strong>OR</strong> </em>34 «kHz» ✓</p>
<p>«recognition that there are two shifts so» change in<em> f</em> = 2 «kHz» <em><strong>OR</strong> f</em> = 37 «kHz» <em><strong>OR</strong> </em>33 «kHz» ✓</p>
<p> </p>
<p><em>Allow a range of 9.3 to 9.5 for <strong>MP1</strong></em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong>.</em></p>
<p><em><strong>MP4</strong> can also be found by applying the Doppler effect twice.</em></p>
<div class="question_part_label">b.</div>
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<h2 style="margin-top: 1em">Examiners report</h2>
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<p>ai) The majority managed to answer this question correctly.</p>
<p>aii) A very well answered question where most worked correctly from the formula for the period of oscillation of a spring.</p>
<p>aiii) Quite a few answers had <em>v</em><sub>max</sub> from the wrong test.</p>
<p>aiv) Most common answers were a correct 2 peak curve, a correct 1 peak curve and a sine curve. Several alternatives were included in the MS as the original data provided in the question was inconsistent, i.e. 44 J is not the maximum kinetic energy available for the second test, and that was taken into account not to disadvantage any candidate´s interpretation.</p>
<p>b) Many got the first three marks for a correct Doppler shift calculation from the correct speed. . There were very few good correct full answers, might be a question to look at for 6/7 during grading.</p>
<div class="question_part_label">a.i.</div>
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[N/A]
<div class="question_part_label">a.ii.</div>
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[N/A]
<div class="question_part_label">a.iii.</div>
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[N/A]
<div class="question_part_label">a.iv.</div>
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[N/A]
<div class="question_part_label">b.</div>
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