6.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{b01b3a41-3ed1-4104-b20d-4cfb845df4a1-11_664_786_221_587}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}

Figure 3 shows a uniform rod $A B$, of length $2 l$ and mass $4 m$. A particle of mass $2 m$ is attached to the rod at $B$. The rod can turn freely in a vertical plane about a fixed smooth horizontal axis through $A$. One end of a light elastic spring, of natural length $2 l$ and modulus of elasticity $k m g$, where $k > 4$, is attached to the rod at $B$. The other end of the spring is attached to a fixed point $C$ which is vertically above $A$, where $A C = 2 l$. The angle $B A C$ is $2 \theta$, where $\frac { \pi } { 6 } < \theta \leqslant \frac { \pi } { 2 }$
\begin{enumerate}[label=(\alph*)]
\item Show that the potential energy of the system is

$$4 m g l \left\{ ( k - 4 ) \sin ^ { 2 } \theta - k \sin \theta \right\} + \text { constant }$$

Given that there is a position of equilibrium with $\theta \neq \frac { \pi } { 2 }$
\item show that $k > 8$

Given that $k = 10$
\item determine the stability of this position of equilibrium.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M4 2016 Q6 [16]}}