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

Damped and forced oscillations, resonance — practice question

A light spring hangs from a fixed point, and a bar magnet is fixed to the lower end of the spring, as shown in Fig. 1.1. To protect the magnet from draughts, a cardboard cup is positioned around it without making contact. The magnet is then displaced vertically and released. Fig. 1.2 shows the way the vertical displacement $y$ of the magnet varies with time $t$.
(a(i))[2]

For the magnet’s oscillations, read Fig. 1.2 to determine the angular frequency $\omega$.

(a(ii))[2]

Show that the oscillating magnet has a maximum kinetic energy of $6.4\,\text{mJ}$.

(b(i))[3]

The cardboard cup is now swapped for one made from aluminium foil. Over $10$ full oscillations of the magnet, the amplitude of vibration falls to $0.75\,\text{cm}$ from the value shown in Fig. 1.2. The change in angular frequency is negligible. Using Faraday’s law of electromagnetic induction, explain why the oscillation amplitude decreases.

(b(ii))[2]

Show that the energy lost by the oscillating magnet is $4.8\,\text{mJ}$.

(c)[2]

The aluminium cup in (b) has mass $6.2\,\text{g}$. Aluminium has a specific heat capacity of $910\,\text{J kg}^{-1}\text{K}^{-1}$. The energy found in (b)(ii) is transferred to the cup as thermal energy. Calculate the mean rise in temperature of the cup.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: Apply $\omega = 2\pi f$ or $\omega = \frac{2\pi}{T}$ with $f = \frac{1}{T}$

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