File "simple-pendulum.html"
Path: /StudyIB/physics/page/273/simple-pendulumhtml
File size: 52.13 KB
MIME-type: text/html
Charset: utf-8
<!DOCTYPE html><html lang="EN"><head> <script>(function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); })(window,document,'script','dataLayer','GTM-PZBWZ8J');</script> <title>Simple pendulum</title><!-- Removed by WebCopy --><!--<base href="/">--><!-- Removed by WebCopy --><meta http-equiv="x-ua-compatible" content="IE=Edge"><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1"><link href="../../../css/bootstrap.flatly.min.css" rel="stylesheet" media="screen"><link rel="stylesheet" href="../../../fonts/awesome/css/font-awesome.min.css"><link href="../../../js/jquery-fancybox/jquery.fancybox.min.css" type="text/css" rel="stylesheet"><link rel="stylesheet" href="../../../css/style.min.css?v=202301301645"><meta name="robots" content="index, follow"><meta name="googlebot" content="noarchive"><meta prefix="og: http://ogp.me/ns#" property="og:title" name="og:title" content="StudyIB Physics: Simple pendulum"> <meta prefix="og: http://ogp.me/ns#" property="og:image" content="https://studyib.net/img/studyib-card-default.jpg"> <meta prefix="og: http://ogp.me/ns#" property="og:description" name="og:description" content="It may be called the simple pendulum but deriving the equation for its motion isn't easy."> <meta prefix="og: http://ogp.me/ns#" property="og:url" name="og:url" content="https://studyib.net/physics/page/273/simple-pendulum"> <meta prefix="og: http://ogp.me/ns#" property="og:site_name" name="og:site_name" content="StudyIB - Your IB learning companion"> <meta prefix="og: http://ogp.me/ns#" property="og:locale" name="og:locale" content="en"> <meta prefix="og: http://ogp.me/ns#" property="og:type" name="og:type" content="website"> <meta name="description" content="It may be called the simple pendulum but deriving the equation for its motion isn't easy."> <meta name="image" content="https://studyib.net/img/studyib-card-default.jpg"> <meta name="keywords" content="StudyIB, Physics, Site overview, Self-study, Videos, Virtual tutor, Practices, Multiple Choice, IB, IBDP, InThinking, International Baccalaureate, Revision, Revision websites, Student Sites, Students, Learning, Guidance, Exam, Questions"> <meta itemprop="name" content="StudyIB Physics: Simple pendulum"> <meta itemprop="description" content="It may be called the simple pendulum but deriving the equation for its motion isn't easy."> <meta itemprop="image" content="https://studyib.net/img/studyib-card-default.jpg"> <meta name="twitter:card" content="summary_large_image"> <meta name="twitter:title" content="StudyIB Physics: Simple pendulum"> <meta name="twitter:description" content="It may be called the simple pendulum but deriving the equation for its motion isn't easy."> <meta name="twitter:image" content="https://studyib.net/img/studyib-card-default.jpg"> <meta name="twitter:creator" content="@inthinker"><link rel="stylesheet" href="../../../css/snippets.min.css?v=202209111300"><link rel="stylesheet" href="../../../css/article.min.css?v=202211221000"><link rel="stylesheet" type="text/css" href="../../../js/slick-carousel/slick.min.css"><link rel="stylesheet" type="text/css" href="../../../js/slick-carousel/slick-theme.min.css"><style type="text/css">button.gifffer img { margin-bottom: 40px !important; }</style><style type="text/css">.filter-sl-only { display: none; }</style><script src="../../../ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script><script src="../../../js/ifvisible.min.js"></script><script>ifvisible.setIdleDuration(300);</script><link rel="apple-touch-icon-precomposed" sizes="57x57" href="../../../img/favicon/apple-touch-icon-57x57.png"> <link rel="apple-touch-icon-precomposed" sizes="114x114" href="../../../img/favicon/apple-touch-icon-114x114.png"> <link rel="apple-touch-icon-precomposed" sizes="72x72" href="../../../img/favicon/apple-touch-icon-72x72.png"> <link rel="apple-touch-icon-precomposed" sizes="144x144" href="../../../img/favicon/apple-touch-icon-144x144.png"> <link rel="apple-touch-icon-precomposed" sizes="60x60" href="../../../img/favicon/apple-touch-icon-60x60.png"> <link rel="apple-touch-icon-precomposed" sizes="120x120" href="../../../img/favicon/apple-touch-icon-120x120.png"> <link rel="apple-touch-icon-precomposed" sizes="76x76" href="../../../img/favicon/apple-touch-icon-76x76.png"> <link rel="apple-touch-icon-precomposed" sizes="152x152" href="../../../img/favicon/apple-touch-icon-152x152.png"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-196x196.png" sizes="196x196"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-96x96.png" sizes="96x96"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-32x32.png" sizes="32x32"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-16x16.png" sizes="16x16"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-128.png" sizes="128x128"> <meta name="application-name" content="StudyIB: Your IB Learning Companion"> <meta name="msapplication-TileColor" content="#A5BED5"> <meta name="msapplication-TileImage" content="/img/favicon/mstile-144x144.png"> <meta name="msapplication-square70x70logo" content="/img/favicon/mstile-70x70.png"> <meta name="msapplication-square150x150logo" content="/img/favicon/mstile-150x150.png"> <meta name="msapplication-wide310x150logo" content="/img/favicon/mstile-310x150.png"> <meta name="msapplication-square310x310logo" content="/img/favicon/mstile-310x310.png"><script>var stdHash = "6da675cbcb3d25f050b05557349abc79", stdTicket = "082b9c9c4ae3624d";</script><script src="../../../js/user/local-stats.min.js?v=202205311700"></script><link href="../../../css/subjects-frontpage.min.css?v=202302031000" rel="stylesheet"></head><body class="public physics"> <noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PZBWZ8J" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript> <div id="top-header"> <div class="wmap general hidden-sm hidden-xs subjects"> <div class="layout-wrapper"> <div class="container-fluid"> <a href=""> <img class="header-thinker" src="../../../img/header-thinker.svg"> </a> <h1> <a href="../../../physics.html"> IBDP Physics </a> <a href="https://inthinking.net" title="inthinking.net" class="inthinking-logo pull-right"> <img src="../../../img/header-logo.svg" style="height: 80px; width: auto;"> </a> </h1> <p class="slogan">InThinking Revision Sites for students</p> <p class="author">Website by <strong>Chris Hamper & Emma Mitchell</strong></p> <p class="updated">Updated 3 February 2023</p> </div> </div> </div> <nav id="public-topnav" class="navbar navbar-default"> <div class="container-fluid"> <div class="navbar-header"> <a class="navbar-brand hidden-md hidden-lg" href="../../../index.htm"> <img class="header-xs-thinker" src="../../../img/header-thinker.svg"> </a> <button type="button" class="collapsed navbar-toggle" data-toggle="collapse" data-target="#subject-navbar-collapse" aria-expanded="false"> <span class="sr-only">Toggle navigation</span> <i class="fa fa-fw fa-2x fa-user"></i> </button> <div class="brand hidden-lg hidden-md hidden-sm"> <a class="brand-xs" href="../../../physics.html"> <strong class="title" style="white-space: nowrap;font-size: 18px;">Physics</strong> </a> </div> </div> <div class="collapse navbar-collapse" id="subject-navbar-collapse"> <ul class="nav navbar-bar navbar-userbox hidden-md hidden-lg"><li class="dropdown"><a href="#" class="dropdown-toggle" data-toggle="dropdown"><i class="fa fa-fw fa-lg fa-user-circle" style="margin-right: 5px;"></i><span style="font-size: 16px;"></span></a><ul class="dropdown-menu"><li class="dropdown-submenu"><a class="dropdown-toggle" href="#" data-toggle="dropdown"><i class="fa fa-fw fa-globe"></i> Subjects</a><ul class="dropdown-menu"><li></li><li class=""><a href="../../../biology.html">DP Biology</a></li><li class=""><a href="../../../chemistry.html">DP Chemistry</a></li><li class=""><a href="../../../englishalanglit.html">DP English A: Language & Literature</a></li><li class=""><a href="../../../mathsanalysis.html">DP Maths: Analysis & Approaches</a></li><li class=""><a href="../../../mathsapplications.html">DP Maths: Applications & Interpretations SL</a></li><li class="active"><a href="../../../physics.html"><i class="fa fa-caret-right"></i> DP Physics</a></li><li class=""><a href="../../../spanishb.html">DP Spanish B</a></li></ul></li><li class="menu-item"><a href="../../../user.html"><i class="fa fa-fw fa-dashboard"></i> Dashboard</a></li><li class="menu-item"><a href="../../../user/profile.html"><i class="fa fa-fw fa-cog"></i> My profile</a></li><li class="menu-item"><a href="../../../user/messages.html"><i class="fa fa-fw fa-envelope"></i> Messages</a></li><li class="menu-item hidden-md hidden-lg mt-xs-3"><a href="../../../index.htm?logout=1" class="btn btn-primary btn-xs-block"><i class="fa fa-fw fa-lg fa-power-off text-danger"></i>Log out</a></li></ul></li></ul> <ul class="nav navbar-bar"><li class=""><a class="home" href="../../../physics.html"><i class="fa fa-fw fa-home"></i> Home</a></li><li class=""><a class="topics" href="#"><i class="fa fa-fw fa-th-large"></i> Topics</a></li><li class=""><a class="favorites" href="../../../physics.html"><i class="fa fa-fw fa-star"></i> My favorites</a></li><li class=""><a class="" href="../../flashcards.html"><i class="fa fa-fw fa-bolt"></i> Flashcards</a></li><li class=""><a class="qbank" href="../../test-your-knowledge.html"><i class="fa fa-fw fa-question"></i> Question bank</a></li><li class=""><a class="networks" href="../../networks.html"><i class="fa fa-fw fa-graduation-cap"></i> Virtual tutor</a></li><li class=""><a class="" href="../../blogs.html"><i class="fa fa-fw fa-paperclip"></i> Blog</a></li><li class=""><a class="sitemap" href="../../sitemap.html"><i class="fa fa-fw fa-sitemap"></i> Sitemap</a></li><li class=""><a class="activity" href="../../../physics.html"><i class="fa fa-fw fa-calendar-check-o"></i> My activity</a></li></ul> <ul class="nav navbar-bar navbar-right"> <li> <form class="navbar-form hidden-md hidden-lg" role="search" method="get" action="physics/search"> <div class="input-group"> <input class="form-control nav-search" name="glob" type="search" placeholder="Search..."> <span class="input-group-btn"> <button type="submit" class="btn bg-blue"> <i class="fa fa-search"> </i> </button> </span> </div> </form> <a href="#" class="toggle-menu-search hidden-sm hidden-xs" data-toggle="dropdown"> <i class="fa fa-lg fa-search"></i> </a> </li></ul> </div> </div></nav><nav id="nav-menu-search" class="shadow-bottom hidden-sm hidden-xs" style="display: none;"> <div class="container-fluid"> <form class="" role="search" method="get" action="physics/search"> <input class="form-control nav-search" name="glob" type="search" placeholder="Search Physics..."> <button class="btn btn-sm btn-primary" type="submit"> Search </button> </form> </div></nav><div class="modal fade" tabindex="-1" role="dialog" id="modal-mini-login"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-body"> <button aria-hidden="true" data-dismiss="modal" class="close hidden-xs login-button-close" type="button">×</button> <form method="post"> <div class="form-group"> <input name="user-email" class="form-control" type="text" placeholder="Email"> </div> <div class="form-group"> <input name="user-password" class="form-control" type="password" placeholder="Password"> <input name="user-fp" class="fp" value="d8c893da5db7501669ffeeac46273ba6" type="hidden"> </div> <div class="form-group"> <a href="../../../reset-password.html" class="reset-password" style="font-weight: normal;"> Forgot your password? </a> </div> <div class="form-group"> <button type="submit" name="submit-login" value="1" class="btn btn-primary btn-block text-center"> <i class="fa fa-user fa-fw"></i> Log in </button> </div> </form> </div> </div> </div></div></div><div class="modal fade" id="show-topics" tabindex="-1" role="dialog"><div id="dialog-topics" class="modal-dialog modal-dialog-topics"><div class="modal-content"><div class="modal-body modal-body-topics"><div id="new-frontpage-toplevels-topics" class="frontpage-box"><div class="row"><div class="col-md-4 col-sm-4"><div class="item"><a href="../3015/free-access-weekend.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Free Access Weekend!</h3></div><div class="body"><div class="cropper" style="background-image: url('../../free.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../814/start-here.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Start here</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/getting-started/getting-started.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../819/revision-tips.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Revision tips</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/getting-started/exam-tips.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../2885/exam-questions.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Exam questions</h3></div><div class="body"><div class="cropper" style="background-image: url('../../practice-papers/flash-front.png'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../204/basics.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Basics</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/basics/basics.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../217/mechanics.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Mechanics</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/mechanics/mechanics.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../252/thermal.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Thermal</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/thermal/thermal.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../444/oscillations-and-waves.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Oscillations & waves</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/waves/waves.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../445/electricity-and-magnetism.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Electricity & magnetism</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/electricity/electricity.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../443/circular-motion-and-gravity.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Circular motion & gravity</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/circular-motion/circular.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../354/atomic-nuclear-and-particles.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Atomic, nuclear & particles</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/atomic/atomic.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../446/energy-production.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Energy production</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/energy-production/energy.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../848/options.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Options</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/astro/options.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../823/astrophysics.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Astrophysics</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/astro/black-hole.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../849/engineering.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Engineering</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/engineering/lift-off.jpg'); height: 10vw;"></div></div></a></div></div></div></div></div></div></div></div><div class="container-fluid shadow-ith"><div class="row frontpage"> <div class="col-md-3" id="left-column"> <p class="visible-xs-block"></p><div class="dropdown user-menu hidden-xs" style="margin-bottom: 20px;"> <button type="button" class="btn btn-default dropdown-toggle" data-toggle="dropdown" style="border-radius: 0; padding: 6px 18px;"> <i class="fa fa-fw fa-user-circle"></i> <small><i class="fa fa-caret-down"></i></small> </button> <ul class="dropdown-menu"> <li class="dropdown-submenu"><a href="#"><i class="fa fa-fw fa-globe"></i> Subjects</a><ul id="user-subjects-menu" class="dropdown-menu"><li></li><li class=""><a href="../../../biology.html">DP Biology</a></li><li class=""><a href="../../../chemistry.html">DP Chemistry</a></li><li class=""><a href="../../../englishalanglit.html">DP English A: Language & Literature</a></li><li class=""><a href="../../../mathsanalysis.html">DP Maths: Analysis & Approaches</a></li><li class=""><a href="../../../mathsapplications.html">DP Maths: Applications & Interpretations SL</a></li><li class="active"><a href="../../../physics.html"><i class="fa fa-caret-right"></i> DP Physics</a></li><li class=""><a href="../../../spanishb.html">DP Spanish B</a></li></ul></li><li class="divider"></li><li><a href="../../../user.html"><i class="fa fa-fw fa-dashboard"></i> Dashboard</a></li><li><a href="../../../user/profile.html"><i class="fa fa-fw fa-cog"></i> My profile</a></li><li><a href="../../../user/messages.html"><i class="fa fa-fw fa-envelope"></i> Messages</a></li> <li class="divider"></li> <li> <a href="../../../index.htm?logout=1"> <i class="fa fa-fw fa-power-off"></i> Log out </a> </li> </ul></div> <div id="side-nav"><h4 class="side-nav-title dropdown"><a href="../444/oscillations-and-waves.html" class="dropdown-toggle toplevel-dropdown" data-toggle="dropdown"><i class="fa fa-ellipsis-v"></i></a> <a href="../444/oscillations-and-waves.html">Oscillations and waves</a><ul class="dropdown-menu"><li><a href="../../../physics.html" style="padding-left: 5px; border-bottom: solid 1px #ddd"><i class="fa fa-fw fa-home"></i> Home</a></li><li><a href="../3015/free-access-weekend.html"><i class="fa fa-fw fa-caret-right"></i> Free Access Weekend!</a></li><li><a href="../814/start-here.html"><i class="fa fa-fw fa-caret-right"></i> Start here</a></li><li><a href="../819/revision-tips.html"><i class="fa fa-fw fa-caret-right"></i> Revision tips</a></li><li><a href="../2885/exam-questions.html"><i class="fa fa-fw fa-caret-right"></i> Exam questions</a></li><li><a href="../204/basics.html"><i class="fa fa-fw fa-caret-right"></i> Basics</a></li><li><a href="../217/mechanics.html"><i class="fa fa-fw fa-caret-right"></i> Mechanics</a></li><li><a href="../252/thermal.html"><i class="fa fa-fw fa-caret-right"></i> Thermal</a></li><li><a href="../445/electricity-and-magnetism.html"><i class="fa fa-fw fa-caret-right"></i> Electricity and magnetism</a></li><li><a href="../443/circular-motion-and-gravity.html"><i class="fa fa-fw fa-caret-right"></i> Circular motion and gravity</a></li><li><a href="../354/atomic-nuclear-and-particles.html"><i class="fa fa-fw fa-caret-right"></i> Atomic, nuclear and particles</a></li><li><a href="../446/energy-production.html"><i class="fa fa-fw fa-caret-right"></i> Energy production</a></li><li><a href="../848/options.html"><i class="fa fa-fw fa-caret-right"></i> Options</a></li><li><a href="../823/astrophysics.html"><i class="fa fa-fw fa-caret-right"></i> Astrophysics</a></li><li><a href="../849/engineering.html"><i class="fa fa-fw fa-caret-right"></i> Engineering</a></li></ul><div class="pull-right"><a class="sidenav-expand" title="Expand all" href="#"><i class="fa fa-plus-circle"></i></a> <a class="sidenav-compress" title="Compress all" href="#"><i class="fa fa-minus-circle"></i></a></div></h4><ul class="side-nav level-0"><li class="expanded parent"><label style="padding-left: 0px"><a class="expander" href="#" style="font-size: .9em"><i class="fa fa-fw fa-caret-right"></i></a><a href="../272/oscillations.html">Oscillations</a></label><ul class="side-nav level-1"><li class="expanded parent selected"><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="simple-pendulum.html">Simple pendulum</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../276/mass-on-a-spring.html">Mass on a spring</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../274/equations-for-shm.html">Equations for SHM</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../275/shm-and-energy.html">SHM and energy</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../277/phase.html">Phase</a></label></li></ul></li><li class=""><label style="padding-left: 0px"><a class="expander" href="#" style="font-size: .9em"><i class="fa fa-fw fa-caret-right"></i></a><a href="../278/waves.html">Waves</a></label><ul class="side-nav level-1"><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../279/introduction-to-waves.html">Introduction to waves</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../365/wave-phenomena.html">Wave phenomena</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../280/graphical-representation-of-waves.html">Graphical representation of waves</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../281/standing-waves-on-a-string.html">Standing waves on a string</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../283/sound.html">Sound</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../284/light.html">Light</a></label></li></ul></li><li class=""><label style="padding-left: 0px"><a class="expander" href="#" style="font-size: .9em"><i class="fa fa-fw fa-caret-right"></i></a><a href="../1128/ahl-waves.html">AHL Waves</a></label><ul class="side-nav level-1"><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../1122/doppler-effect.html">Doppler effect</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../1117/simple-harmonic-motion.html">Simple harmonic motion</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../1127/single-slit-diffraction.html">Single slit diffraction</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../1123/resolution.html">Resolution</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../1126/multiple-slit-interference.html">Multiple slit interference</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../1124/thin-film-interference.html">Thin film interference</a></label></li></ul></li></ul></div> <div class="hidden-xs hidden-sm"> <button class="btn btn-default btn-block text-xs-center" data-toggle="modal" data-target="#modal-feedback" style="margin-bottom: 10px"><i class="fa fa-send"></i> Feedback</button> </div> </div> <div class="col-md-9" id="main-column"> <h1 class="page_title"> Simple pendulum <a href="#" class="mark-page-favorite pull-right" data-pid="273" title="Mark as favorite" onclick="return false;"><i class="fa fa-star-o"></i></a> </h1> <ol class="breadcrumb"> <li><a href="../../../physics.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../444/oscillations-and-waves.html">Oscillations and waves</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../272/oscillations.html">Oscillations</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Simple pendulum</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 10 minutes"><i class="fa fa-clock-o"></i> 10'</span> </ol> <article id="main-article"> <p><img alt="" src="../../waves/shm.jpg" style="float: left; width: 250px; height: 166px;">It may be called the simple pendulum but deriving the equation for its motion isn't easy.</p> <p>The trick is to realise that, for the pendulum to continue swinging as it moves through the equililbrium position, the tension in the string is greater than the weight of the mass. </p> <hr class="hidden-separator"> <div class="panel panel-turquoise panel-has-colored-body"> <div class="panel-heading"> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <div> <p>If a hanging ball is displaced to one side and released, it will swing backwards and forwards. This is because there is a <em>restoring</em> force that always points back towards the equilibrium position. If the swings are small, this force is proportional to the displacement, thus obeying simple harmonic motion.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/167720176"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <div> <p>Consider the forces acting on a pendulum bob. We can show that, for small swings, the acceleration is proportional to displacement and always directed towards the equilibrium position.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/167751601"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test Yourself</p> </div> </div> <div class="panel-body"> <div> <p><i>Use quizzes to practise application of theory.</i></p> <br><a class="btn btn-primary btn-block text-center" data-toggle="modal" href="#225d6fc4"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="225d6fc4"> <div class="modal-dialog" style="width: 95vw; max-width: 960px"> <div class="modal-content"> <div class="modal-header slide-quiz-title"> <h4 class="modal-title" style="width: 100%;"> Pendulums <strong class="q-number pull-right"> <span class="counter">1</span>/<span class="total">1</span> </strong> </h4> </div> <div class="modal-body p-xs-3"> <div class="slide-quiz" data-stats="6-80-273" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>Simple harmonic motion is when:</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> The moon goes around the earth</label></p><p><label class="radio"><input type="radio"> A child swings on a rope</label></p><p><label class="radio"><input class="c" type="radio"> A pendulum swings with small amplitude</label></p><p><label class="radio"><input type="radio"> A birds wing moves up and down</label></p></div><div class="q-explanation"><p>Specifically small amplitude swings</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of the following are SHM</p><p style="text-align: center;"><img alt="" class="gifffer" data-gifffer="/media/physics/images/pendulagif.gif" style="width: 315px; height: 144px;"></p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> None but B is closest</label></p><p><label class="radio"><input type="radio"> All</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> A and B</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> just B</label></p></div><div class="q-explanation"><p>B has small amplitude so is appproximately SHM</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p style="text-align: center;"><img alt="" class="gifffer" data-gifffer="/media/physics/images/pendulagif.gif" style="width: 315px; height: 144px;"></p><p>Which pendulum has the biggest frequency?</p></div><div class="q-answer"><p><label class="radio" style=" float: left; margin-right: 40px; "><input class="c" type="radio"> C</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> A</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> B</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> D</label></p></div><div class="q-explanation"><p>C completes most cycles per unit time</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p style="text-align: center;"><img alt="" class="gifffer" data-gifffer="/media/physics/images/pendulagif.gif" style="width: 315px; height: 144px;"></p><p>Which pendulum has the longest time period?</p></div><div class="q-answer"><p><label class="radio" style=" float: left; margin-right: 40px; "><input class="c" type="radio"> D</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> A</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> B</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> C</label></p></div><div class="q-explanation"><p>D takes the longest time to complete a full cycle</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p style="text-align: center;"><img alt="" class="gifffer" data-gifffer="/media/physics/images/pendulagif.gif" style="width: 315px; height: 144px;"></p><p>Which pendulum has the largest amplitude?</p></div><div class="q-answer"><p><label class="radio" style=" float: left; margin-right: 40px; "><input class="c" type="radio"> D</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> A</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> B</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> C</label></p></div><div class="q-explanation"><p>The distance from the equilibrium position to maximum displacement is largest in D</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p style="text-align: center;"><img alt="" class="gifffer" data-gifffer="/media/physics/images/pendulagif.gif" style="width: 315px; height: 144px;"></p><p>In which pendulum will the tension in the strinmg reach the largest value?</p></div><div class="q-answer"><p><label class="radio" style=" float: left; margin-right: 40px; "><input class="c" type="radio"> D</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> A</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> B</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> C</label></p></div><div class="q-explanation"><p>This is a tricky one.</p><p>The tension is greatest at the bottom of the swing and depends velocity<sup>2</sup>/radius. D has the highest velocity but also the longest radius. However the higher velocity outweighs the larger radius so D has the biggest tension.</p><p>The simplest way to answer this is to use your intuition, which would be the most difficult to hold?</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The pendulum below is swinging to the left</p><p style="text-align: center;"><img alt="" src="../../images/pendulum1.jpg" style="width: 237px; height: 237px;"></p><p>The direction of the resultant force is</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> down</label></p><p><label class="radio"><input class="c" type="radio"> right</label></p><p><label class="radio"><input type="radio"> left</label></p><p><label class="radio"><input type="radio"> up</label></p></div><div class="q-explanation"><p>The force will act towards the equilibrium position</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The pendulum below is at the furthest point to the left</p><p style="text-align: center;"><img alt="" src="../../images/pendulum3.jpg" style="width: 230px; height: 230px;"></p><p>The resultant force is</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> Minimum and towards the right</label></p><p><label class="radio"><input class="c" type="radio"> Maximum and towards the right</label></p><p><label class="radio"><input type="radio"> zero</label></p><p><label class="radio"><input type="radio"> Maximum and towards the left</label></p></div><div class="q-explanation"><p>Restoring force is proportional to displacement and directed towards the equilibrium position.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The pendulum below is moving to the right</p><p style="text-align: center;"><img alt="" src="../../images/pendulum2.jpg" style="width: 225px; height: 225px;"></p><p>The resultant force is</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> upwards</label></p><p><label class="radio"><input type="radio"> zero</label></p><p><label class="radio"><input type="radio"> downwards</label></p><p><label class="radio"><input type="radio"> rightwards</label></p></div><div class="q-explanation"><p>The pendulum bob is moving along the arc of a circle so there is a force towards the centre.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The pendulum bob below is at rest</p><p style="text-align: center;"><img alt="" src="../../images/pendulum2.jpg" style="width: 225px; height: 225px;"></p><p>The resultant force is</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> horizontal</label></p><p><label class="radio"><input type="radio"> up</label></p><p><label class="radio"><input class="c" type="radio"> zero</label></p><p><label class="radio"><input type="radio"> down</label></p></div><div class="q-explanation"><p>Forces are balanced</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>If the pendulum amplitude is very small we can assume that</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> The resultant force is zero</label></p><p><label class="radio"><input type="radio"> The resultant force is constant</label></p><p><label class="radio"><input class="c" type="radio"> The forces are balanced as it passes through the centre</label></p><p><label class="radio"><input type="radio"> There is no acceleration</label></p></div><div class="q-explanation"><p>In deriving the equation we assume that T = mg at the equilibrium position</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The equation for the time period of a simple pendulum is</p><p><span class="tib-mathml"></span></p><p><span class="tib-mathml"><math display="block"> <semantics> <mrow> <mi>T</mi><mo>=</mo><mn>2</mn><mi>π</mi><msqrt> <mrow> <mfrac> <mi>L</mi> <mi>g</mi> </mfrac> </mrow> </msqrt> </mrow> <annotation encoding="MathType-MTEF">MathType@MTEF@5@5@+=faaagCart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedmvETj2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8FesqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9Gqpi0dc9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamivaiabg2da9iaaikdacqaHapaCdaGcaaqaamaalaaabaGaamitaaqaaiaadEgaaaaaleqaaaaa@3459@</annotation> </semantics></math></span> If the time period of a pendulum is 0.5s, The length of the string is increased by a factor 4 the time period will be</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> 1 s</label></p><p><label class="radio"><input type="radio"> 2 s</label></p><p><label class="radio"><input type="radio"> 0.125 s</label></p><p><label class="radio"><input type="radio"> 0.25 s</label></p></div><div class="q-explanation"><p>T is proportional to √4 so will be 2x bigger</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The equation for the time period of a simple pendulum is</p><p><span class="tib-mathml"></span></p><p><span class="tib-mathml"><math display="block"> <semantics> <mrow> <mi>T</mi><mo>=</mo><mn>2</mn><mi>π</mi><msqrt> <mrow> <mfrac> <mi>L</mi> <mi>g</mi> </mfrac> </mrow> </msqrt> </mrow> <annotation encoding="MathType-MTEF">MathType@MTEF@5@5@+=faaagCart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedmvETj2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8FesqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9Gqpi0dc9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamivaiabg2da9iaaikdacqaHapaCdaGcaaqaamaalaaabaGaamitaaqaaiaadEgaaaaaleqaaaaa@3459@</annotation> </semantics></math></span> The time period of a pendulum is 0.5s, if the pendulum is taken to the moon the time period will be</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 0.02 s</label></p><p><label class="radio"><input class="c" type="radio"> 1.2 s</label></p><p><label class="radio"><input type="radio"> 3 s</label></p><p><label class="radio"><input type="radio"> 0.5 s</label></p></div><div class="q-explanation"><p>g on the moon is about 1/6 that on Earth</p><p>T is proportional to 1/√g so T = 0.5 x √6</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The equation for the time period of a simple pendulum is</p><p><span class="tib-mathml"></span></p><p><span class="tib-mathml"><math display="block"> <semantics> <mrow> <mi>T</mi><mo>=</mo><mn>2</mn><mi>π</mi><msqrt> <mrow> <mfrac> <mi>L</mi> <mi>g</mi> </mfrac> </mrow> </msqrt> </mrow> <annotation encoding="MathType-MTEF">MathType@MTEF@5@5@+=faaagCart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedmvETj2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8FesqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9Gqpi0dc9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamivaiabg2da9iaaikdacqaHapaCdaGcaaqaamaalaaabaGaamitaaqaaiaadEgaaaaaleqaaaaa@3459@</annotation> </semantics></math></span> Ihe time period of a pendulum is 0.5s, if the mass is doubled the time period will be</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> 0.5 s</label></p><p><label class="radio"><input type="radio"> 1 s</label></p><p><label class="radio"><input type="radio"> 0.125 s</label></p><p><label class="radio"><input type="radio"> 0.25 s</label></p></div><div class="q-explanation"><p>The time period does not depend on mass.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The equation for the time period of a simple pendulum is</p><p><span class="tib-mathml"></span></p><p><span class="tib-mathml"><math display="block"> <semantics> <mrow> <mi>T</mi><mo>=</mo><mn>2</mn><mi>π</mi><msqrt> <mrow> <mfrac> <mi>L</mi> <mi>g</mi> </mfrac> </mrow> </msqrt> </mrow> <annotation encoding="MathType-MTEF">MathType@MTEF@5@5@+=faaagCart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedmvETj2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8FesqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9Gqpi0dc9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamivaiabg2da9iaaikdacqaHapaCdaGcaaqaamaalaaabaGaamitaaqaaiaadEgaaaaaleqaaaaa@3459@</annotation> </semantics></math></span> The frequency of a pendulum is 1 Hz The length of the string is increased by a factor 4 the frequency will be</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 1 Hz</label></p><p><label class="radio"><input type="radio"> 2 Hz</label></p><p><label class="radio"><input type="radio"> 0.25 Hz</label></p><p><label class="radio"><input class="c" type="radio"> 0.5 Hz</label></p></div><div class="q-explanation"><p>f= 1/T so f is proportional to 1/√L so if L is x4, f will be x 1/2</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div> </div> </div> <div class="modal-footer slide-quiz-actions"> <div class=""> <div class="pull-left pull-xs-none mb-xs-3"> <button class="btn btn-default d-xs-none btn-prev"> <i class="fa fa-arrow-left"></i> Prev </button> </div> <div class="pull-right pull-xs-none"> <button class="btn btn-success btn-xs-block text-xs-center btn-results" style="display: none"> <i class="fa fa-bar-chart"></i> Check Results </button> <button class="btn btn-default d-xs-none btn-next"> Next <i class="fa fa-arrow-right"></i> </button> <button class="btn btn-default btn-xs-block text-xs-center btn-close" data-dismiss="modal" style="display: none"> Close </button> </div> </div> </div> </div> </div></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="page-container panel-self-assessment" data-id="273"> <div class="panel-heading">MY PROGRESS</div> <div class="panel-body understanding-rate"> <div class="msg"></div> <label class="label-lg">Self-assessment</label><p>How much of <strong>Simple pendulum</strong> have you understood?</p><div class="slider-container text-center"><div id="self-assessment-slider" class="sib-slider self-assessment " data-value="1" data-percentage=""></div></div> <label class="label-lg">My notes</label> <textarea name="page-notes" class="form-control" rows="3" placeholder="Write your notes here..."></textarea> </div> <div class="panel-footer text-xs-center"> <span id="last-edited" class="mb-xs-3"> </span> <div class="actions mt-xs-3"> <button id="save-my-progress" type="button" class="btn btn-sm btn-primary text-center btn-xs-block"> <i class="fa fa-fw fa-floppy-o"></i> Save </button> </div> </div></div> <div id="modal-feedback" class="modal fade" tabindex="-1" role="dialog"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <h4 class="modal-title">Feedback</h4> <button type="button" class="close hidden-xs hidden-sm" data-dismiss="modal" aria-label="Close"> <span aria-hidden="true">×</span> </button> </div> <div class="modal-body"> <div class="errors"></div> <p><strong>Which of the following best describes your feedback?</strong></p> <form method="post" style="overflow: hidden"> <div class="form-group"> <div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Recommendation"> Recommend</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Problem"> Report a problem</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Improvement"> Suggest an improvement</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Other"> Other</label></div> </div> <hr> <div class="row"> <div class="col-md-6"> <div class="form-group"> <label for="feedback-name">Name</label> <input type="text" class="form-control" name="feedback-name" placeholder="Name" value=" "> </div> </div> <div class="col-md-6"> <div class="form-group"> <label for="feedback-email">Email address</label> <input type="email" class="form-control" name="feedback-email" placeholder="Email" value="@airmail.cc"> </div> </div> </div> <div class="form-group"> <label for="feedback-comments">Comments</label> <textarea class="form-control" name="feedback-comments" style="resize: vertical;"></textarea> </div> <input type="hidden" name="feedback-ticket" value="082b9c9c4ae3624d"> <input type="hidden" name="feedback-url" value="https://studyib.net/physics/page/273/simple-pendulum"> <input type="hidden" name="feedback-subject" value="6"> <input type="hidden" name="feedback-subject-name" value="Physics"> <div class="pull-left"> </div> </form> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary btn-xs-block feedback-submit mb-xs-3 pull-right"> <i class="fa fa-send"></i> Send </button> <button type="button" class="btn btn-default btn-xs-block m-xs-0 pull-left" data-dismiss="modal"> Close </button> </div> </div> </div></div> </article> <hr class="hidden-md hidden-lg"> <div class="hidden-md hidden-lg mt-xs-3"> <button class="btn btn-default btn-block text-xs-center" data-toggle="modal" data-target="#modal-feedback" style="margin-bottom: 10px"><i class="fa fa-send"></i> Feedback</button> </div> </div> <input type="hidden" id="user-id" value="38342"></div><input id="ticket" type="hidden" value="082b9c9c4ae3624d"><input id="tzoffset" type="hidden" value="new"><input id="fp" class="fp" type="hidden" value=""></div><div id="std-footer"> <div class="wmap"> <div class="layout-wrapper"> <p> <a href="https://www.inthinking.net"> © <span id="footer-year"></span> <em>InThinking</em> <script>document.getElementById("footer-year").innerHTML = new Date().getFullYear();</script> </a> | <a target="_self" href="../../../about.html"> About us </a> | <a target="_self" href="../../../terms-and-conditions.html"> Legal </a> | <a target="_self" href="../../../contact.html"> Contact </a> </p> <p> <a class="social" target="_blank" href="https://twitter.com/#!/inthinker"> <img src="../../../img/social/twitter-square.svg"> Twitter </a> <a class="social" target="_blank" href="https://www.facebook.com/inthinking.net"> <img src="../../../img/social/facebook-square.svg"> Facebook </a> <a class="social" target="_blank" href="https://www.linkedin.com/profile/view?id=139741989"> <img src="../../../img/social/linkedin-square.svg"> LinkedIn </a> </p> </div> </div></div><script src="../../../js/jquery-1.11.3.min.js"></script><script src="../../../js/bootstrap.min.js"></script><script src="../../../js/jquery-fancybox/jquery.fancybox.min.js"></script><script>var pageId = 273;</script><script type="text/javascript" src="../../../js/jqueryui/jquery-ui-custom.min.js"></script><script type="text/javascript" src="../../../js/jqueryui/jquery.ui.touch-punch.js"></script><script type="text/javascript" src="../../../js/std-quizzes-helpers.min.js?v=20220406"></script><script src="../../../ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script><script type="text/javascript" src="../../../js/slick-carousel/slick.min.js"></script><script type="text/javascript" src="../../../js/std-slide-quizzes.min.js?v=20220406"></script><script src="../../../js/gifffer/gifffer.min.js"></script><script src="../../../js/gifffer/gifffer-player.min.js?v=20201126"></script><script type="text/javascript" src="../../../js/jqueryui/jquery-ui.min.js"></script><script type="text/javascript" src="../../../js/jqueryui/jquery.ui.touch-punch.min.js"></script><script src="../../../js/user/page-my-progress.min.js?v=202211221000"></script><script>var sAJAX='/pages/subjects/activity/user-stats-page.php?t=082b9c9c4ae3624d&p=273&s=6&x=19303';var sData='k4iA6GSB03BgPm14aDORPHpsE3KeSVBAEzP5PHpsE39FIxiA6GSB0bfjSYyBPm1F93B87YyBPVpBWnfLWVK8PFAF7YcHEKvr6GSDPmjn6GyDEzAFWGcrE0ij6GyDPmjn6GyDEzAF7bKFEYv86GB2Pm1FPFAF7YcrZxP5PBAh7Ysq73Bm7LAh7YcHEKAhOm7D0xvDZGLAWY987YK2EVKRSGrFeC==';var loopSecs = 30;var minSecsLog = 60;var lsKey = '6-83610-273';</script><script src="../../../js/subjects/activity/user-stats-page.min.js?v=202205311700"></script><script src="../../../js/subjects/activity/my-favorites.min.js?v=20220610"></script><script src="../../../js/subjects/feedback.min.js?v=202211221000"></script><script>var sessionUpdateSecs = 300;</script><script type="text/javascript" src="../../../js/session-updater.js"></script><script>(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');ga('create', 'UA-98480796-3', 'auto');ga('send', 'pageview');</script><script src="../../../js/devicefp/devicefp.min.js"></script><script src="../../../js/jq-quickfit/jq-quickfit.min.js?v=20220201"></script><script src="../../../js/frontpage-subjects.min.js?v=202211161300"></script><script type="text/javascript" src="../../../js/studyib-jq.min.js?v=202211241300"></script><script type="text/javascript">$(document).ready(function(){ $('#trigger-modal-video-overview').click(function() { if( $('#modal-video-overview .modal-body iframe').attr('src').length == 0 ) { $('#modal-video-overview .modal-body iframe').attr('src', 'https://www.youtube.com/embed/hxxtdiLdTFk?rel=0'); } }); $('#modal-video-overview').on('hidden.bs.modal', function() { $('#modal-video-overview .modal-body iframe').attr('src', ''); }); });</script></body></html>