Probability — practice question

One end of a light elastic string with natural length $3\ \text{m}$ and modulus of elasticity $24\ \text{N}$ is fixed at point $O$. A particle $P$ of mass $0.4\ \text{kg}$ is attached to the free end of the string. $P$ is projected vertically downwards from $O$ at an initial speed of $2\ \text{m s}^{-1}$. When the string has extension $x\ \text{m}$, the speed of $P$ is $v\ \text{m s}^{-1}$.