One end of a light elastic spring, of natural length 0.8 m and modulus of elasticity 40 N , is attached to a fixed point \(O\). The spring hangs vertically, at rest, with particles of masses 2 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 kg particle begins to move upwards.

1. Show that the 2 kg particle performs simple harmonic motion about its equilibrium position with period \(\frac { 2 } { 5 } \pi \mathrm {~s}\). State the distance below \(O\) of the centre of the oscillations.
   The speed of the 2 kg particle is \(0.4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) when its displacement from the centre of oscillation is 0.06 m .
2. Find the amplitude of the motion.
3. Deduce the value of \(M\).