Probability — practice question

A light elastic string with natural length $0.4\text{ m}$ and modulus of elasticity $20\text{ N}$ has one end fixed at point $A$ on a smooth plane inclined at $30^\circ$ to the horizontal. Its other end is fastened to a particle $P$ of mass $0.5\text{ kg}$, which is initially in equilibrium on the plane. From that equilibrium position, $P$ is projected down the plane with speed $5\text{ m s}^{-1}$. When the particle is moving at $2\text{ m s}^{-1}$ for the first time, the string has extension $e\text{ m}$.