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 \(A P B\) 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 \(A P\) in terms of \(m, g, l\) and \(\omega\).