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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 Time zone 2
Command term Sketch 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 \(\frac{{{\text{energy stored}}}}{{{\text{power loss}}}}\) 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 \(\frac{\pi }{2}\) or 90º or \(\frac{1}{4}\) period

 

Do not penalize sign of phase difference.

Do not accept \(\frac{\lambda }{4}\) for MP2

[2 marks]

b.i.

resonant f = 0.125 « Hz »

\(\frac{{25}}{{\left( {2\pi  \times 0.125} \right)}}\) = 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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