Physics 9702 · AS & A Level · Simple harmonic oscillations

Simple harmonic oscillations — practice question

A pendulum is formed by a metal sphere P hanging from a fixed point on a thread, as shown in Fig. 3.1. The centre of gravity of sphere P is a distance $L$ from the fixed point. The sphere is displaced to one side and then let go, so that it oscillates. It may be assumed to oscillate with simple harmonic motion.
(a)[2]

State what simple harmonic motion means.

(b)[3]

Fig. 3.2 shows the variation of the velocity $v$ of sphere P with the displacement $x$ from its mean position. Use Fig. 3.2 to determine the frequency $f$ of the oscillations of sphere P.

(c)[2]

The period $T$ of the oscillations of sphere P is given by $T = 2\pi\sqrt{\frac{L}{g}}$, where $g$ is the acceleration of free fall. Use your answer in (b) to find the length $L$.

(d)[2]

A second pendulum has a sphere Q suspended from a thread. Spheres P and Q are identical. The thread supporting sphere Q is longer than the thread attached to sphere P. Sphere Q is displaced and then released. The oscillations of sphere Q have the same amplitude as the oscillations of sphere P. On Fig. 3.2, sketch the variation of the velocity $v$ with displacement $x$ for sphere Q.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Acceleration is proportional to displacement

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