Physics 9702 · AS & A Level · Damped and forced oscillations, resonance
Damped and forced oscillations, resonance — practice question
A sphere made of heavy metal with mass $0.81\,\text{kg}$ hangs on a string. It moves in small side-to-side oscillations, as illustrated in Fig. 4.1. These oscillations 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 angular frequency of the oscillations.
(b(ii))[2]
Calculate the total energy of the oscillations.
(c)[3]
The sphere is then lowered into water. It is moved sideways by $+0.036\,\text{m}$ from equilibrium and released at $t = 0$. The water makes the motion of the sphere critically damped. On Fig. 4.2, sketch how the displacement $x$ of the sphere from equilibrium varies with $t$ from $t = 0$ to $t = 6.0\,\text{s}$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Acceleration is directly proportional to displacement” …