5 A light elastic string has natural length 3 m and modulus of elasticity 45 N . A particle \(P\) of mass 0.6 kg is attached to the mid-point of the string. The ends of the string are attached to fixed points \(A\) and \(B\) which lie on a line of greatest slope of a smooth plane inclined at \(30 ^ { \circ }\) to the horizontal. The distance \(A B\) is 4 m , and \(A\) is higher than \(B\).

1. Calculate the distance \(A P\) when \(P\) rests on the slope in equilibrium.
   \(P\) is released from rest at the point between \(A\) and \(B\) where \(A P = 2.5 \mathrm {~m}\).
2. Find the maximum speed of \(P\).
3. Show that \(P\) is at rest when \(A P = 1.6 \mathrm {~m}\).