Representation of data — practice question

A particle $P$ of mass $0.5\,\text{kg}$ is fired along a smooth horizontal surface in the direction of a fixed point $A$. At the outset, $P$ is at $O$ on the surface, and after projection its displacement from $O$ is $x\,\text{m}$ and its velocity is $v\,\text{m s}^{-1}$. Particle $P$ is attached to $A$ by a light elastic string with natural length $0.8\,\text{m}$ and modulus of elasticity $16\,\text{N}$. The distance $OA$ is $1.6\,\text{m}$ (see diagram). The motion of $P$ is opposed by a force of magnitude $24x^2\,\text{N}$.