3 A particle \(P\) of mass \(m\) is attached to one end of a light inextensible string of length \(a\). The other end of the string is attached to a fixed point \(O\). The path of the particle is a complete vertical circle with centre \(O\). When \(P\) is at its lowest point, its speed is \(u\). When \(P\) is at the point \(A\), the tension in the string is \(T\) and the string makes an angle \(\theta\) with the downward vertical, where \(\cos \theta = \frac { 3 } { 5 }\). When \(P\) is at the point \(B\), above the level of \(O\), the tension in the string is \(\frac { 1 } { 8 } T\) and angle \(B O A = 90 ^ { \circ }\). Find \(u\) in terms of \(a\) and \(g\).