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Date	November 2016	Marks available	2	Reference code	16N.3.HL.TZ0.14
Level	Higher level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Draw	Question number	14	Adapted from	N/A

Question

A mass-spring system is forced to vibrate vertically at the resonant frequency of the system. The motion of the system is damped using a liquid.

At time t=0 the vibrator is switched on. At time t_B the vibrator is switched off and the system comes to rest. The graph shows the variation of the vertical displacement of the system with time until t_B.

Explain, with reference to energy in the system, the amplitude of oscillation between

(i) t = 0 and t_A.

(ii) t_A and t_B.

[2]

a.

The system is critically damped. Draw, on the graph, the variation of the displacement with time from t_B until the system comes to rest.

[2]

b.

Markscheme

i

amplitude is increasing as energy is added

ii

energy input = energy lost due to damping

a.

curve from time t_B reaching zero displacement

in no more than one cycle

Award zero if displacement after t_B goes to negative values.

b.

Examiners report

[N/A]

a.

[N/A]

b.

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)

Option B: Engineering physics