Physics 9702 · AS & A Level · Simple harmonic oscillations
Simple harmonic oscillations — practice question
A hollow tube, sealed at one end, has a cross-sectional area $A$ of $24\,\text{cm}^2$. Sand is added to the tube so that the combined mass $M$ of the tube and the sand is $0.23\,\text{kg}$. The tube floats upright in a liquid of density $\rho$, as shown in Fig. 3.1. The depth of the bottom of the tube below the liquid surface is $h$. The tube is moved vertically and then released. Fig. 3.2 shows how the depth $h$ changes with time $t$.
(a(i))[1]
Determine the amplitude, in metres, of the oscillations.
(a(ii))[2]
Determine the frequency of oscillation of the tube in the liquid.
(a(iii))[2]
Determine the acceleration of the tube when $h$ is a maximum.
(b)[2]
The frequency $f$ of oscillation of the tube is given by $f = \frac{1}{2\pi}\sqrt{\frac{A\rho g}{M}}$, where $g$ is the acceleration of free fall. Calculate the density $\rho$ of the liquid in which the tube is floating.
(c)[3]
The oscillations shown in Fig. 3.2 are undamped. In practice, the liquid produces light damping. On Fig. 3.2, draw a line to represent light damping of the oscillations from time $t = 0$ to time $t = 1.4\,\text{s}$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The amplitude is $0.020\,\text{m}$.” …