4. A uniform \(\operatorname { rod } A B\), of mass \(m\) and length \(2 a\), is free to rotate in a vertical plane about a fixed smooth horizontal axis through \(A\) and perpendicular to the plane. The rod hangs in equilibrium with \(B\) below \(A\). The rod is rotated through a small angle and released from rest at time \(t = 0\).

1. Show that the motion of the rod is approximately simple harmonic.
2. Using this approximation, find the time \(t\) when the rod is first vertical after being released.
   (Total 6 marks)