7.
\begin{figure}[h]
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\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{a20270d9-4a30-45d8-ac33-2e4fc9c7fb06-10_487_696_316_632}
\end{figure}
A light elastic string, of natural length \(3 l\) and modulus of elasticity \(\lambda\), has its ends attached to two points \(A\) and \(B\), where \(A B = 3 l\) and \(A B\) is horizontal. A particle \(P\) of mass \(m\) is attached to the mid-point of the string. Given that \(P\) rests in equilibrium at a distance \(2 l\) below \(A B\), as shown in Figure 1,
- show that \(\lambda = \frac { 15 m g } { 16 }\).
The particle is pulled vertically downwards from its equilibrium position until the total length of the elastic string is \(7.8 l\). The particle is released from rest.
- Show that \(P\) comes to instantaneous rest on the line \(A B\).