2. A uniform square lamina \(S\) has side \(2 a\). The radius of gyration of \(S\) about an axis through a vertex, perpendicular to \(S\), is \(k\).
- Show that \(k ^ { 2 } = \frac { 8 a ^ { 2 } } { 3 }\).
The lamina \(S\) is free to rotate in a vertical plane about a fixed smooth horizontal axis which is perpendicular to \(S\) and passes through a vertex.
- By writing down an equation of rotational motion for \(S\), find the period of small oscillations of \(S\) about its position of stable equilibrium.