8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3b070338-1de4-4c33-be29-d37ac06c9fed-28_200_1086_214_552}
\captionsetup{labelformat=empty}
\caption{Figure 7}
\end{figure}
The fixed points \(A\) and \(B\) lie on a smooth horizontal surface with \(A B = 6 \mathrm {~m}\).
A particle \(P\) has mass 0.3 kg .
One end of a light elastic string, of natural length 2 m and modulus of elasticity 20 N , is attached to \(P\), and the other end is attached to \(A\).
One end of another light elastic string, of natural length 2 m and modulus of elasticity 40 N , is attached to \(P\) and the other end is attached to \(B\).
The particle \(P\) is at rest in equilibrium at the point \(E\) on the surface, as shown in Figure 7.
- Show that \(E B = \frac { 8 } { 3 } \mathrm {~m}\).
The particle \(P\) is now held at the midpoint of \(A B\) and released from rest.
- Show that \(P\) oscillates with simple harmonic motion about the point \(E\).
The time between the instant when \(P\) is released and the instant when it first returns to the point \(E\) is \(S\) seconds.
- Find the exact value of \(S\).
- Find the length of time during one oscillation for which the speed of \(P\) is more than \(2 \mathrm {~ms} ^ { - 1 }\)