Physics 9702 · AS & A Level · Simple harmonic oscillations
Simple harmonic oscillations — practice question
This dish is formed from part of a hollow glass sphere. It is secured to a horizontal table and holds a small solid ball of mass $45\,\text{g}$, as shown in Fig. 4.1. The ball’s horizontal displacement from the centre $C$ of the dish is $x$. At the beginning, the ball is kept at rest with $x = 3.0\,\text{cm}$. It is then released. Fig. 4.2 shows how the horizontal displacement $x$ of the ball from point $C$ changes with time $t$. The ball’s motion in the dish is simple harmonic, with acceleration $a$ given by $a = -\left(\frac{g}{R}\right)x$, where $g$ is the acceleration of free fall and $R$ is a constant that depends on the dimensions of the dish and the ball.
(a)[1]
Use Fig. 4.2 to demonstrate that the angular frequency $\omega$ of the ball’s oscillation in the dish is $2.9\,\text{rad s}^{-1}$.
(b(i))[2]
Use the result from (a) to find $R$.
(b(ii))[2]
Calculate the ball’s speed as it moves across the centre $C$ of the dish.
(c)[3]
Moisture gathers on the dish surface, causing the ball’s motion to become lightly damped. On the axes in Fig. 4.2, draw a line showing the ball’s lightly damped motion during the first $5.0\,\text{s}$ after release.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use of $\omega = \dfrac{2\pi}{T}$” …