3 One end of a light elastic string of natural length 0.4 m and modulus of elasticity 20 N is attached to a fixed point \(A\) on a smooth plane inclined at \(30 ^ { \circ }\) to the horizontal. The other end of the string is attached to a particle \(P\) of mass 0.5 kg which rests in equilibrium on the plane.

1. Calculate the extension of the string.
   \(P\) is projected down the plane from the equilibrium position with speed \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The extension of the string is \(e \mathrm {~m}\) when the speed of the particle is \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) for the first time.
2. Find \(e\).