5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8a687d17-ec7e-463f-84dd-605f5c230db1-16_720_232_251_858}
\captionsetup{labelformat=empty}
\caption{Figure 6}
\end{figure}
The fixed points, \(A\) and \(B\), are a distance \(10 a\) apart, with \(B\) vertically above \(A\).
One end of a light elastic string, of natural length \(2 a\) and modulus of elasticity \(2 m g\), is attached to a particle \(P\) of mass \(m\) and the other end is attached to \(A\).
One end of another light elastic string, of natural length \(4 a\) and modulus of elasticity \(6 m g\), is attached to \(P\) and the other end is attached to \(B\).
The particle \(P\) rests in equilibrium at the point \(C\), as shown in Figure 6.
- Show that each string has an extension of \(2 a\).
(5)
The particle \(P\) is now pulled down vertically, so that it is a distance \(a\) below \(C\) and then released from rest. - Show that in the subsequent motion, \(P\) performs simple harmonic motion.
- Find, in terms of \(a\) and \(g\), the speed of \(P\) when it is a distance \(\frac { 7 } { 2 } a\) above \(A\).