Problem

A particle $P$ of mass $m$ is attached to two light inextensible strings each of length $l$. The end of one string is attached to a fixed point $A$ and the end of the other string is attached to a fixed point $B$, with $A$ vertically above $B$. Angle $APB$ is a right angle. The particle $P$ rotates in a horizontal circle at a constant angular speed $\omega$ with both strings taut (see diagram).

Find the tension in string $AP$ in terms of $m$, $g$, $l$ and $\omega$.