Probability — practice question

One end of a light elastic string, whose natural length is $0.3\,\text{m}$ and whose modulus of elasticity is $6\,\text{N}$, is fastened to a fixed point $O$ on a smooth horizontal plane. Its other end is attached to a particle $P$ of mass $0.2\,\text{kg}$, and $P$ travels on the plane in a circular path with centre $O$. The angular speed of $P$ is $\omega\,\text{rad s}^{-1}$.