Probability — practice question

One end of a light elastic string, whose modulus of elasticity is $15\,\text{N}$, is fastened to a fixed point $A$, which lies $2\,\text{m}$ directly above a fixed small smooth ring $R$. The string’s natural length is $2\,\text{m}$, and it passes through $R$. Its other end is attached to a particle $P$ of mass $m\,\text{kg}$, and $P$ travels at constant angular speed $\omega\,\text{rad s}^{-1}$ around a horizontal circle with centre $0.4\,\text{m}$ vertically below the ring. $PR$ forms an acute angle $\theta$ with the vertical (see diagram).