For the magnet’s oscillations, read Fig. 1.2 to determine the angular frequency $\omega$.
Show that the oscillating magnet has a maximum kinetic energy of $6.4\,\text{mJ}$.
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.
Show that the energy lost by the oscillating magnet is $4.8\,\text{mJ}$.
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.