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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.

M17/4/PHYSI/HP3/ENG/TZ2/11

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.

[2]

a.

State and explain the displacement of the sine wave vibrator at t = 8.0 s.

[2]

b.i.

The vibrator is switched off and the spring continues to oscillate. The Q factor is 25.

Calculate the ratio $\frac{energy stored}{power loss}$ $\frac{{{\text{energy stored}}}}{{{\text{power loss}}}}$ for the oscillations of the spring–mass system.

[2]

b.ii.

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]

a.

displacement of vibrator is 0

because phase difference is $\frac{π}{2}$ $\frac{\pi }{2}$ or 90^º or $\frac{1}{4}$ $\frac{1}{4}$ period

Do not penalize sign of phase difference.

Do not accept $\frac{λ}{4}$ $\frac{\lambda }{4}$ for MP2

[2 marks]

b.i.

resonant f = 0.125 « Hz »

$\frac{25}{(2 π \times 0.125)}$ $\frac{{25}}{{\left( {2\pi \times 0.125} \right)}}$ = 32 «s»

Watch for ECF from MP1 to MP2.

[2 marks]

b.ii.

Examiners report

[N/A]

a.

[N/A]

b.i.

[N/A]

b.ii.

Syllabus sections

Option B: Engineering physics » Option B: Engineering physics (Additional higher level option topics) » B.4 – Forced vibrations and resonance (HL only)

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Option B: Engineering physics » Option B: Engineering physics (Additional higher level option topics)

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