Physics 9702 · AS & A Level · Energy in simple harmonic motion

Energy in simple harmonic motion — practice question

As shown in Fig. 3.1, a metal ball hangs from a fixed point on a string. The ball is then given a slight displacement and released. Fig. 3.2 shows how the displacement $x$ of the ball changes with time $t$.
(a(i))[1]

State two instants when the ball’s speed is at a maximum.

(a(ii))[2]

Show that the ball’s maximum speed is about $0.08\ \text{m s}^{-1}$.

(b(i))[2]

Fig. 3.3 shows how the potential energy $E_p$ of the ball’s oscillations varies with displacement $x$. On the axes in Fig. 3.3, sketch a graph to show how the kinetic energy of the ball varies with displacement $x$.

(b(ii))[2]

The amplitude of the oscillations decreases over a long time. After many oscillations, the amplitude is $0.60\ \text{cm}$. Use Fig. 3.3 to find the total energy of the ball’s oscillations for an amplitude of $0.60\ \text{cm}$. Explain your working.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Any two correct times, such as $0.30\ \text{s}$, $0.90\ \text{s}$ or $1.50\ \text{s}$

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