4 A particle \(P\) of mass 0.2 kg is suspended from a fixed point \(O\) by a light elastic string of natural length 0.7 m and modulus of elasticity \(3.5 \mathrm {~N} . P\) is at the equilibrium position when it is projected vertically downwards with speed \(1.6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). At time \(t \mathrm {~s}\) after being set in motion \(P\) is \(x \mathrm {~m}\) below the equilibrium position and has velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. Show that the equilibrium position of \(P\) is 1.092 m below \(O\).
2. Prove that \(P\) moves with simple harmonic motion, and calculate the amplitude.
3. Calculate \(x\) and \(v\) when \(t = 0.4\).