Probability — practice question

The natural length of a light elastic string is $2.2\,\text{m}$, and its modulus of elasticity is $14.3\,\text{N}$. A particle $P$ of mass $m\,\text{kg}$ is fixed to the midpoint of the string. The string ends are fixed at points $A$ and $B$, which are $2.4\,\text{m}$ apart and lie at the same horizontal level. $P$ is released from rest at the midpoint of $AB$. During the motion that follows, $P$ reaches its maximum speed at a point $0.5\,\text{m}$ below $AB$.