7 Two particles \(A\) and \(B\) are connected by a light inextensible string of length 1.26 m . Particle \(A\) has a mass of 1.25 kg and moves on a smooth horizontal table in a circular path of radius 0.9 m and centre \(O\). The string passes through a small smooth hole at \(O\). Particle \(B\) has a mass of 2 kg and moves in a horizontal circle as shown in the diagram. The angle that the portion of string below the table makes with the downwards vertical through \(O\) is \(\theta\), where \(\cos \theta = \frac { 4 } { 5 }\) (see diagram).
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1. Determine the angular speed of \(A\) and the angular speed of \(B\). At the start of the motion, \(A , O\) and \(B\) all lie in the same vertical plane.
2. Find the first subsequent time when \(A , O\) and \(B\) all lie in the same vertical plane.