Question 11 EITHER alternative.

One end of a light elastic spring, of natural length \(0.8\ \mathrm{m}\) and modulus of elasticity \(40\ \mathrm{N}\), is attached to a fixed point \(O\). The spring hangs vertically, at rest, with particles of masses \(2\ \mathrm{kg}\) and \(M\ \mathrm{kg}\) attached to its free end. The \(M\ \mathrm{kg}\) particle becomes detached from the spring, and as a result the \(2\ \mathrm{kg}\) particle begins to move upwards.

(i) Show that the \(2\ \mathrm{kg}\) particle performs simple harmonic motion about its equilibrium position with period \(\frac25\pi\ \mathrm{s}\). State the distance below \(O\) of the centre of the oscillations.

The speed of the \(2\ \mathrm{kg}\) particle is \(0.4\ \mathrm{m\ s^{-1}}\) when its displacement from the centre of oscillation is \(0.06\ \mathrm{m}\).

(ii) Find the amplitude of the motion.

(iii) Deduce the value of \(M\).