5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bb73b211-7629-4ed7-9b71-91841c29bb85-16_193_931_269_520}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Two fixed points \(A\) and \(B\) are 5 m apart on a smooth horizontal floor. A particle \(P\) of mass 0.5 kg is attached to one end of a light elastic string, of natural length 2 m and modulus of elasticity 20 N . The other end of the string is attached to \(A\). A second light elastic string, of natural length 1.2 m and modulus of elasticity 15 N , has one end attached to \(P\) and the other end attached to \(B\).
Initially \(P\) rests in equilibrium at the point \(O\), as shown in Figure 3.
- Show that \(A O = 3 \mathrm {~m}\).
The particle is now pulled towards \(A\) and released from rest at the point \(C\), where \(A C B\) is a straight line and \(O C = 1 \mathrm {~m}\).
- Show that, while both strings are taut, \(P\) moves with simple harmonic motion.
- Find the speed of \(P\) at the instant when the string \(P B\) becomes slack.
The particle first comes to instantaneous rest at the point \(D\).
- Find the distance \(D B\).