$\displaystyle A$ is a fixed point at a height $\displaystyle H$ above a perfectly inelastic smooth horizontal plane. A light inextensible string of length $\displaystyle L(>H)$ has one end attached to $\displaystyle A$ and other is to a heavy particle. The particle is held at the level of $\displaystyle A$ with string just taut and released from rest. Find the height of the particle above the plane when it is next instantaneously at rest.