Physics 9702 · AS & A Level · Damped and forced oscillations, resonance
Damped and forced oscillations, resonance — practice question
A U-tube is filled with liquid, as illustrated in Fig. 4.1. The overall length of the liquid column is $L$. The column is then moved so that the change in level from the equilibrium position in each arm of the U-tube is $x$, as shown in Fig. 4.2. The liquid in the U-tube then oscillates with acceleration $a$ given by $a = -\left( \frac{2g}{L} \right) x$, where $g$ is the acceleration of free fall.
(a)[2]
Show that the liquid column undergoes simple harmonic motion.
(b)[3]
The displacement $x$ varies with time $t$ as shown in Fig. 4.3. Use the information in Fig. 4.3 to find the length $L$ of the liquid column.
(c(i))[1]
The oscillations in Fig. 4.3 are damped. Suggest one reason for this damping.
(c(ii))[2]
Calculate the ratio $\dfrac{\text{total energy of oscillations after }1.5\text{ complete oscillations}}{\text{total initial energy of oscillations}}$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Defining equation of SHM: $a = -kx$ or $a \propto -x$” …