7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b99b3eb0-9bca-42e3-bea9-3b0454a872db-24_177_876_260_593}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
The fixed points \(A\) and \(B\) are 7 m apart on a smooth horizontal surface.
A light elastic string has natural length 2 m and modulus of elasticity 4 N . One end of the string is attached to a particle \(P\) of mass 2 kg and the other end is attached to \(A\)
Another light elastic string has natural length 3 m and modulus of elasticity 2 N . One end of this string 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 4.
- Show that \(O A = 2.5 \mathrm {~m}\).
The particle \(P\) now receives an impulse of magnitude 6Ns in the direction \(O B\)
- Show that \(P\) initially moves with simple harmonic motion with centre \(O\)
- Determine the amplitude of this simple harmonic motion.
The point \(C\) lies on \(O B\). As \(P\) passes through \(C\) the string attached to \(B\) becomes slack.
- Find the speed of \(P\) as it passes through \(C\)
- Find the time taken for \(P\) to travel directly from \(O\) to \(C\)