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

Damped and forced oscillations, resonance — practice question

A bar magnet with mass $180\,\text{g}$ is hung from the free end of a spring, as shown in Fig. 2.1. The magnet is positioned so that one pole lies close to the middle of a coil of wire. The coil is joined in series with a resistor and a switch, and the switch is open. The magnet is moved vertically and then released so that it oscillates, with one pole staying inside the coil and the other pole remaining outside it. At time $t = 0$, the magnet is oscillating freely as it goes through its equilibrium position. At time $t = 3.0\,\text{s}$, the switch in the circuit is closed. The graph in Fig. 2.2 shows how the vertical displacement $y$ of the magnet varies with time $t$.
(a)[2]

Determine, to two significant figures, the frequency of oscillation of the magnet.

(b)[1]

State whether closing the switch causes light, heavy or critical damping.

(c)[6]

Calculate the change in the oscillation energy $\Delta E$ of the magnet between $t = 2.7\,\text{s}$ and $t = 7.5\,\text{s}$. Explain your working.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Period obtained e.g. $T = \frac{3}{2.5}$

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI