A bar magnet of mass 
is suspended from the free end of a spring, as illustrated in the figure below.
The magnet hangs so that one pole is near the centre of a coil of wire. The coil is connected in series with a resistor and a switch. The switch is open. The magnet is displaced vertically and then allowed to oscillate with one pole remaining inside the coil. The other pole remains outside the coil. At time 
, the magnet is oscillating freely as it passes through its equilibrium position. At time 
, the switch in the circuit is closed. The variation with time 
of the vertical displacement 
of the magnet is shown in the graph below.
Determine, to two significant figures, the frequency of oscillation of the magnet.
Calculate the change in the energy 
of oscillation of the magnet between time 
and time 
. Explain your working.
.
.
