7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{23e6a9ae-bf00-45a3-b462-e18760d9af45-24_655_890_239_529}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows four uniform rods, each of mass \(m\) and length \(2 a\). The rods are freely hinged at their ends to form a rhombus \(A B C D\). Point \(A\) is attached to a fixed point on a ceiling and the rhombus hangs freely with \(C\) vertically below \(A\). A light elastic spring of natural length \(2 a\) and modulus of elasticity \(7 m g\) connects the points \(A\) and \(C\). A particle of mass \(3 m\) is attached to point \(C\).
- Show that, when \(A D\) is at an angle \(\theta\) to the downward vertical, the potential energy \(V\) of the system is given by
$$V = 28 m g a \cos ^ { 2 } \theta - 48 m g a \cos \theta + \text { constant }$$
Given that \(\theta > 0\)
- find the value of \(\theta\) for which the system is in equilibrium,
- determine the stability of this position of equilibrium.