6. A uniform circular disc, of mass \(m\), radius \(a\) and centre \(O\), is free to rotate in a vertical plane about a fixed smooth horizontal axis. The axis passes through the mid-point \(A\) of a radius of the disc.

1. Find an equation of motion for the disc when the line \(A O\) makes an angle \(\theta\) with the downward vertical through \(A\).
   (5)
2. Hence find the period of small oscillations of the disc about its position of stable equilibrium. When the line \(A O\) makes an angle \(\theta\) with the downward vertical through \(A\), the force acting on the disc at \(A\) is \(\mathbf { F }\).
3. Find the magnitude of the component of \(\mathbf { F }\) perpendicular to \(A O\).
   (5)