A rigid body consists of a thin uniform rod \(A B\), of mass \(4 m\) and length \(6 a\), joined at \(B\) to a point on the circumference of a uniform circular disc, with centre \(O\), mass \(8 m\) and radius \(2 a\). The point \(C\) on the circumference of the disc is such that \(B C\) is a diameter and \(A B C\) is a straight line (see diagram). The body rotates about a smooth fixed horizontal axis through \(C\), perpendicular to the plane of the disc. The angle between \(C A\) and the downward vertical at time \(t\) is denoted by \(\theta\).

1. Given that the body is performing small oscillations about the downward vertical, show that the period of these oscillations is approximately \(16 \pi \sqrt { } \left( \frac { a } { 11 g } \right)\).
2. Given instead that the body is released from rest in the position given by \(\cos \theta = 0.6\), find the maximum speed of \(A\).