5 One end of a light elastic string, of natural length 0.78 m and modulus of elasticity 0.8 mgN , is attached to a fixed point \(O\) on a smooth plane inclined at angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac { 5 } { 13 }\). A particle \(P\) of mass \(m \mathrm {~kg}\) is attached to the other end of the string. \(P\) is released from rest at \(O\) and moves down the plane without reaching the bottom. Find

1. the maximum speed of \(P\) in the subsequent motion,
2. the distance of \(P\) from \(O\) when it is at its lowest point.