5. A uniform square lamina \(A B C D\) of side \(a\) and mass \(m\) is free to rotate in vertical plane about a horizontal axis through \(A\). The axis is perpendicular to the plane of the lamina. The lamina is released from rest when \(t = 0\) and \(A C\) makes a small angle with the downward vertical through \(A\).

1. Show that the moment of inertia of the lamina about the axis is \(\frac { 2 } { 3 } m a ^ { 2 }\).
2. Show that the motion of the lamina is approximately simple harmonic.
3. Find the time \(t\) when \(A C\) is first vertical.