6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f6ab162c-8473-4464-ad62-87a359d85ab3-10_191_972_276_484}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{figure}
The points \(A\) and \(B\) are 3.75 m apart on a smooth horizontal floor. A particle \(P\) has mass 0.8 kg . One end of a light elastic spring, of natural length 1.5 m and modulus of elasticity 24 N , is attached to \(P\) and the other end is attached to \(A\). The ends of another light elastic spring, of natural length 0.75 m and modulus of elasticity 18 N , are attached to \(P\) and \(B\). The particle \(P\) rests in equilibrium at the point \(O\), where \(A O B\) is a straight line, as shown in Figure 5.
- Show that \(A O = 2.4 \mathrm {~m}\).
The point \(C\) lies on the straight line \(A O B\) between \(O\) and \(B\). The particle \(P\) is held at \(C\) and released from rest.
- Show that \(P\) moves with simple harmonic motion.
The maximum speed of \(P\) is \(\sqrt { } 2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
- Find the time taken by \(P\) to travel 0.3 m from \(C\).