Physics 9702 · AS & A Level · Damped and forced oscillations, resonance

Damped and forced oscillations, resonance — practice question

(a)[2]

Distinguish free oscillations from forced oscillations.

(b)

A trolley is supported on a horizontal surface by two stretched springs, as shown in Fig. 4.1. One spring is connected to a fixed point. The other spring is attached to an oscillator that makes the trolley oscillate horizontally. The oscillator vibrates with a constant amplitude of vibration. The frequency of vibration of the oscillator is increased gradually from a very low value. Fig. 4.2 shows the way in which the trolley’s vibration amplitude $x_0$ varies with frequency $f$.

(b(i))[3]

Use Fig. 4.2 to state and explain the trolley’s natural frequency of vibration.

(b(ii))[1]

Use Fig. 4.2 to state whether there are any frictional forces acting on the trolley.

(c)[2]

The oscillator in (b) is now stopped. The trolley is given a horizontal displacement of $4.7\,\text{cm}$ along the line of the springs. The trolley is then released. Use information from Fig. 4.2 to estimate the maximum speed of the trolley.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Free oscillations: no energy loss / no resistive forces

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