Date | May 2017 | Marks available | 2 | Reference code | 17M.3.HL.TZ2.11 |
Level | Higher level | Paper | Paper 3 | Time zone | 2 |
Command term | Calculate | Question number | 11 | Adapted from | N/A |
Question
A driven system is lightly damped. The graph shows the variation with driving frequency f of the amplitude A of oscillation.
A mass on a spring is forced to oscillate by connecting it to a sine wave vibrator. The graph shows the variation with time t of the resulting displacement y of the mass. The sine wave vibrator has the same frequency as the natural frequency of the spring–mass system.
On the graph, sketch a curve to show the variation with driving frequency of the amplitude when the damping of the system increases.
State and explain the displacement of the sine wave vibrator at t = 8.0 s.
The vibrator is switched off and the spring continues to oscillate. The Q factor is 25.
Calculate the ratio energy storedpower lossenergy storedpower loss for the oscillations of the spring–mass system.
Markscheme
lower peak
identical behaviour to original curve at extremes
peak frequency shifted to the left
Award [0] if peak is higher.
For MP2 do not accept curves which cross.
[2 marks]
displacement of vibrator is 0
because phase difference is π2π2 or 90º or 1414 period
Do not penalize sign of phase difference.
Do not accept λ4λ4 for MP2
[2 marks]
resonant f = 0.125 « Hz »
25(2π×0.125)25(2π×0.125) = 32 «s»
Watch for ECF from MP1 to MP2.
[2 marks]