5. A particle \(P\) of mass 0.8 kg is attached to one end \(A\) of a light elastic spring \(O A\), of natural length 60 cm and modulus of elasticity 12 N . The spring is placed on a smooth horizontal table and the end \(O\) is fixed. The particle \(P\) is pulled away from \(O\) to a point \(B\), where \(O B = 85 \mathrm {~cm}\), and is released from rest.

1. Prove that the motion of \(P\) is simple harmonic with period \(\frac { 2 \pi } { 5 }\) s.
2. Find the greatest magnitude of the acceleration of \(P\) during the motion. Two seconds after being released from rest, \(P\) passes through the point \(C\).
3. Find, to 2 significant figures, the speed of \(P\) as it passes through \(C\).
4. State the direction in which \(P\) is moving 2 s after being released.