Physics 9702 · AS & A Level · Simple harmonic oscillations

Simple harmonic oscillations — practice question

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

State the meaning of simple harmonic motion.

(b)[3]

The way in which the velocity $v$ of sphere P changes with displacement $x$ from its mean position is shown in Fig. 3.2. 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 determine the length $L$.

(d)[2]

A second pendulum has a sphere Q suspended by a thread. Spheres P and Q are identical. The thread attached to 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 varies directly with displacement

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