A simple pendulum of length ' \(L\) ' has mass ' \(M\) ' and it oscillates freely with amplitude 'A'. At extreme position, its potential energy is

At extreme position, the potential energy of simple pendulum,
\(\mathrm{PE}=\frac{1}{2} \mathrm{~mA}^2 \omega\)
where, \(\omega=\) angular frequency \(=\frac{2 \pi}{\mathrm{~T}}\)
For simple pendulum, \(T=2 \pi \sqrt{\frac{\mathrm{~L}}{\mathrm{~g}}}\)
\(\therefore \omega=\frac{2 \pi}{2 \pi} \frac{\sqrt{\mathrm{~g}}}{\mathrm{~L}}=\frac{\sqrt{\mathrm{g}}}{\mathrm{~L}} \quad \ldots\left[\because \mathrm{~T}=\frac{2 \pi}{\omega}\right]\)

On putting value of \(\omega\) in Eq. (i), we get
\(\begin{aligned}
& \mathrm{PE}=\frac{1}{2} \mathrm{mM}^2\left(\sqrt{\frac{\mathrm{~g}}{\mathrm{~L}}}\right)^2 \\
& =\frac{\mathrm{mgA}}{}{ }^2 \\
& 2 \mathrm{~L}
\end{aligned}\)