Physics 9702 · AS & A Level · Simple harmonic oscillations

Simple harmonic oscillations — practice question

A trolley of negligible mass that moves without friction is joined to a fixed point $A$ by a spring. A second spring connects the trolley to a variable frequency oscillator, as shown in Fig. 2.1. Both springs stay extended, but still within the limit of proportionality. At the start, the oscillator is switched off. The trolley is moved horizontally along the line joining the two springs and then let go. Fig. 2.2 shows how the trolley’s velocity $v$ varies with time $t$.
(a(i).1)[1]

State two different times, taken from Fig. 2.2, when the trolley’s displacement is zero.

(a(i).2)[1]

State two different times, taken from Fig. 2.2, when the acceleration in one direction is at its greatest.

(a(ii))[2]

Determine the frequency of oscillation of the trolley.

(a(iii))[1]

The displacement of the trolley changes sinusoidally with time. The velocity of the trolley also changes sinusoidally with time. State the phase difference between the displacement and the velocity.

(b)[1]

The oscillator is now switched on. Its vibration amplitude is constant. The vibration frequency $f$ of the oscillator is changed. The trolley is made to oscillate by the vibrations of the oscillator. Fig. 2.3 shows how the amplitude $a_0$ of the trolley’s oscillations varies with $f$. Using your answer to (a), state the approximate frequency at which the amplitude is greatest.

(c)[2]

The amplitude of the oscillation in (b) can be lowered without causing a significant change in the frequency at which the amplitude is greatest. State how this may be done and give a reason for your answer.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Any two valid times: $0.1\,\text{s}, 0.3\,\text{s}, 0.5\,\text{s}$

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