7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2e837bb9-4ada-4f0f-8b21-2730611335f2-24_165_1392_258_338}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{figure}
Figure 5 shows two fixed points, \(A\) and \(B\), which are 5 m apart on a smooth horizontal floor.
A particle \(P\) of mass 1.25 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 \(\lambda\) newtons, has one end attached to \(P\) and the other end attached to \(B\)
Initially \(P\) rests in equilibrium at the point \(O\), where \(A O = 3 \mathrm {~m}\)
- Show that \(\lambda = 15\)
The particle is now projected along the floor towards \(B\)
At time \(t\) seconds, \(P\) is a displacement \(x\) metres from \(O\) in the direction \(O B\) - Show that, while both strings are taut, \(P\) moves with simple harmonic motion where \(\ddot { x } = - 18 x\)
The initial speed of \(P\) is \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
- Find the speed of \(P\) at the instant when the string \(P B\) becomes slack.
Both strings are taut for \(T\) seconds during one complete oscillation.
- Find the value of \(T\)