Representation of data — practice question

A light elastic string with natural length $1.2\,\text{m}$ and modulus of elasticity $24\,\text{N}$ is fixed between points $A$ and $B$ on a smooth horizontal plane, with $AB = 1.2\,\text{m}$. A particle $P$ is attached at the midpoint of the string. $P$ is projected at $0.5\,\text{m s}^{-1}$ across the surface in a direction at right angles to $AB$ (see diagram). $P$ is momentarily at rest when it is $0.25\,\text{m}$ from $AB$.