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Date	May 2019	Marks available	2	Reference code	19M.3.HL.TZ2.14
Level	Higher level	Paper	Paper 3	Time zone	2
Command term	Outline	Question number	14	Adapted from	N/A

Question

A railway track passes over a bridge that has a span of 20 m.

The bridge is subject to a periodic force as a train crosses, this is caused by the weight of the train acting through the wheels as they pass the centre of the bridge.

The wheels of the train are separated by 25 m.

The graph shows the variation of the amplitude of vibration A of the bridge with driving frequency f_D, when the damping of the bridge system is small.

Show that, when the speed of the train is 10 m s-1, the frequency of the periodic force is 0.4 Hz.

[1]

Outline, with reference to the curve, why it is unsafe to drive a train across the bridge at 30 m s^-1 for this amount of damping.

[2]

The damping of the bridge system can be varied. Draw, on the graph, a second curve when the damping is larger.

[2]

Markscheme

time period

T = « $\frac{25}{10}$ » = 2.5 s AND f = $\frac{1}{T}$

evidence of f = $\frac{10}{25}$ ✔

Answer 0.4 Hz is given, check correct working is shown.

30 m s^–1 corresponds to f = 1.2 Hz ✔

the amplitude of vibration is a maximum for this speed

corresponds to the resonant frequency ✔

similar shape with lower amplitude ✔

maximum shifted slightly to left of the original curve ✔

Amplitude must be lower than the original, but allow the amplitude to be equal at the extremes.

Examiners report

The question was correctly answered by almost all candidates.

The answers to this question were generally well presented and a correct argument was presented by almost all candidates. Resonance was often correctly referred to.

A correct curve, with lower amplitude and shifted left, was drawn by most candidates.

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

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