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Date	November 2018	Marks available	2	Reference code	18N.3.HL.TZ0.11
Level	Higher level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Determine	Question number	11	Adapted from	N/A

Question

A mass is attached to a vertical spring. The other end of the spring is attached to the driver of an oscillator.

The mass is performing very lightly damped harmonic oscillations. The frequency of the driver is higher than the natural frequency of the system. At one instant the driver is moving downwards.

State and explain the direction of motion of the mass at this instant.

[2]

a.

The oscillator is switched off. The system has a Q factor of 22. The initial amplitude is 10 cm. Determine the amplitude after one complete period of oscillation.

[2]

b.

Markscheme

because the mass and the driver are out of phase «by $\pi$ » ✔

so upwards ✔

Justification needed for MP2

a.

ALTERNATIVE 1:

« $Q = 2\pi \frac{{A_0^2}}{{A_0^2 - A_1^2}}$ » ⇒ $\frac{{A_1^2}}{{A_0^2}} = 1 - \frac{{2\pi }}{Q}$

$\frac{{{A_1}}}{{{A_0}}} =$ « $\sqrt {1 - \frac{{2\pi }}{{22}}}$ =» A₁ = 8.5 «cm»

ALTERNATIVE 2:

driver amplitude is constant ✔

so mass amplitude is unchanged at 10 cm ✔

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