Probability — practice question

One end of a light elastic string whose natural length is $0.5\,\text{m}$ and whose modulus of elasticity is $12\,\text{N}$ is fastened to a fixed point $O$. The other end is joined to a particle $P$ of mass $0.24\,\text{kg}$. $P$ is projected vertically upwards with speed $3\,\text{m s}^{-1}$ from a point $0.8\,\text{m}$ vertically beneath $O$.