4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ae189c40-0071-4a6b-91eb-8ffebe082a04-12_364_718_278_612}
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\caption{Figure 2}
\end{figure}
The ends of a light elastic string, of natural length \(4 l\) and modulus of elasticity \(\lambda\), are attached to two fixed points \(A\) and \(B\), where \(A B\) is horizontal and \(A B = 4 l\). A particle \(P\) of mass \(2 m\) is attached to the midpoint of the string. The particle hangs freely in equilibrium at a distance \(\frac { 3 } { 2 } l\) vertically below the midpoint of \(A B\), as shown in Figure 2.
- Show that \(\lambda = \frac { 20 } { 3 } m g\).
The particle is pulled vertically downwards from its equilibrium position until the total length of the string is 6l. The particle is then released from rest.
- Show that \(P\) comes to instantaneous rest before reaching the line \(A B\).