7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{698b44b5-801c-45ec-b9de-021e44487edb-24_173_968_223_488}
\captionsetup{labelformat=empty}
\caption{Figure 6}
\end{figure}
The fixed points \(A\) and \(B\) are 4 m apart on a smooth horizontal floor. One end of a light elastic string, of natural length 1.8 m and modulus of elasticity 45 N , is attached to a particle \(P\) and the other end is attached to \(A\). One end of another light elastic string, of natural length 1.2 m and modulus of elasticity 20 N , is attached to \(P\) and the other end is attached to \(B\). The particle \(P\) rests in equilibrium at the point \(O\), where \(A O B\) is a straight line, as shown in Figure 6.
- Show that \(A O = 2.2 \mathrm {~m}\).
The point \(C\) lies on the straight line \(A O B\) with \(A C = 2.7 \mathrm {~m}\). The mass of \(P\) is 0.6 kg . The particle \(P\) is held at \(C\) and then released from rest.
- Show that, while both strings are taut, \(P\) moves with simple harmonic motion with centre \(O\).
The point \(D\) lies on the straight line \(A O B\) with \(A D = 1.8 \mathrm {~m}\). When \(P\) reaches \(D\) the string \(P B\) breaks.
- Find the time taken by \(P\) to move directly from \(C\) to \(A\).