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: “$\omega = 2\pi f$” …