5 A particle \(P\) of mass \(m \mathrm {~kg}\) is attached to one end of a light elastic string of natural length 1.2 m and modulus of elasticity 0.75 mgN . The other end of the string is attached to a fixed point \(O\) of a smooth plane inclined at \(30 ^ { \circ }\) to the horizontal. \(P\) is released from rest at \(O\) and moves down the plane.

1. Show that the maximum speed of \(P\) is reached when the extension of the string is 0.8 m .
2. Find the maximum speed of \(P\).
3. Find the maximum displacement of \(P\) from \(O\).