Probability — practice question

A particle $P$ with mass $0.3\,\text{kg}$ is connected to a fixed point $A$ by a light elastic string whose natural length is $0.8\,\text{m}$ and modulus of elasticity is $16\,\text{N}$. The particle $P$ travels in a horizontal circle with centre $O$. It is given that $AO$ is vertical and that angle $OAP$ is $60^\circ$ (see diagram).