Physics 9702 · AS & A Level · Damped and forced oscillations, resonance
Damped and forced oscillations, resonance — practice question
A liquid occupies a U-shaped tube. In each limb of the tube, the liquid column has length $L$, as shown in Fig. 3.1. The liquid columns are shifted vertically. The liquid then oscillates in the tube. The liquid levels are shown displaced from their equilibrium positions in Fig. 3.2. The acceleration $a$ of the liquid in the tube is linked to the displacement $x$ by $a = -\left(\frac{g}{L}\right)x$, where $g$ is the acceleration of free fall.
(a)[3]
Explain how the expression indicates that the liquid in the tube is carrying out simple harmonic motion.
(b)[3]
The length $L$ of each liquid column is $18\,\text{cm}$. Determine the period $T$ of the oscillations.
(c)[3]
The liquid oscillations in the tube are damped. In any single complete cycle of the oscillations, the amplitude falls by $6.0\%$ of its value at the start of the oscillation. Determine the ratio $\frac{\text{energy of oscillations after 3 cycles}}{\text{initial energy of oscillations}}$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Acceleration is opposite to displacement (negative sign)” …