Probability — practice question

A particle $P$ with mass $0.5\,\text{kg}$ is attached to one end of a light elastic string whose natural length is $0.8\,\text{m}$ and modulus of elasticity is $16\,\text{N}$. The opposite end of the string is fixed at point $O$. Particle $P$ is released from rest at the point $0.8\,\text{m}$ vertically below $O$. When the extension of the string is $x\,\text{m}$, the downward velocity of $P$ is $v\,\text{m s}^{-1}$ and a force of $25x^2\,\text{N}$ opposes the motion of $P$.