Probability — practice question

A particle $P$ with mass $0.4\,\text{kg}$ is fastened to one end of a light elastic string whose natural length is $0.5\,\text{m}$ and modulus of elasticity is $6\,\text{N}$. The opposite end of the string is fixed at point $O$. The particle $P$ is let go from rest at the point $(0.5 + x)\,\text{m}$ vertically below $O$. The particle $P$ then comes to instantaneous rest at $O$.