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

Energy in simple harmonic motion — practice question

A small steel sphere is performing vertical oscillations at the end of a spring, as illustrated in Fig. 4.1. The sphere's velocity $v$ depends on its displacement $x$ from equilibrium as follows $v = \pm 9.7\sqrt{(11.6 - x^2)}$, where $v$ is in $\text{cm s}^{-1}$ and $x$ is in $\text{cm}$.
(a(i))[2]

Calculate the oscillation frequency.

(a(ii))[1]

Show that the oscillation amplitude is $3.4\,\text{cm}$.

(a(iii))[2]

Calculate the sphere’s maximum acceleration $a_0$.

(b)[3]

On Fig. 4.2, sketch how the sphere’s acceleration $a$ changes with $x$.

(c)[3]

Describe, without calculation, how potential energy and kinetic energy are interchanged during the oscillations.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: $\omega = 2\pi f$

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