7.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{23e6a9ae-bf00-45a3-b462-e18760d9af45-24_655_890_239_529}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\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 $C$.
\begin{enumerate}[label=(\alph*)]
\item 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 $\theta > 0$
\item find the value of $\theta$ for which the system is in equilibrium,
\item determine the stability of this position of equilibrium.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M4 2017 Q7 [13]}}