5 A particle \(P\) of mass 0.3 kg is attached to one end of a light elastic string of natural length 0.9 m and modulus of elasticity 18 N . The other end of the string is attached to a fixed point \(O\) which is 3 m above the ground.

1. Find the extension of the string when \(P\) is in the equilibrium position.
   \(P\) is projected vertically downwards from the equilibrium position with initial speed \(6 \mathrm {~ms} ^ { - 1 }\). At the instant when the tension in the string is 12 N the string breaks. \(P\) continues to descend vertically.
2. (a) Calculate the height of \(P\) above the ground at the instant when the string breaks.
   (b) Find the speed of \(P\) immediately before it strikes the ground.