Physics 9702 · AS & A Level · Damped and forced oscillations, resonance

Damped and forced oscillations, resonance — practice question

A solid metal sphere with mass $0.81\,\text{kg}$ hangs on a string. It performs small side-to-side oscillations, as illustrated in Fig. 4.1. The sphere’s motion can be treated as simple harmonic, with amplitude $0.036\,\text{m}$ and period $3.0\,\text{s}$.
(a)[2]

State the meaning of simple harmonic motion.

(b(i))[2]

Calculate the oscillation’s angular frequency.

(b(ii))[2]

Calculate the total energy stored in the oscillations.

(c)[3]

The sphere is then lowered into water. It is displaced sideways by $+0.036\,\text{m}$ from equilibrium and released at time $t = 0$. The water makes the motion critically damped. On Fig. 4.2, sketch how the displacement $x$ of the sphere from equilibrium varies with $t$ from $t = 0$ to $t = 6.0\,\text{s}$.

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This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Acceleration proportional to the displacement

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