Probability — practice question

A light elastic string has natural length $2\,\text{m}$ and modulus of elasticity $39\,\text{N}$. The string’s ends are fastened to fixed points $A$ and $B$, which lie at the same horizontal height and are $2.4\,\text{m}$ apart. A particle $P$ of mass $m\,\text{kg}$ is joined to the midpoint of the string and is in equilibrium at a point $0.5\,\text{m}$ below $AB$ (see diagram).