6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{00388805-5d60-4327-a10e-c0df74a0cb75-11_186_1042_223_452}
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\caption{Figure 3}
\end{figure}
Two points \(A\) and \(B\) are 6 m apart on a smooth horizontal floor. A particle \(P\) of mass 0.5 kg is attached to one end of a light elastic spring, of natural length 2.5 m and modulus of elasticity 20 N . The other end of the spring is attached to \(A\). A second light elastic spring, of natural length 1.5 m and modulus of elasticity 18 N , has one end attached to \(P\) and the other end attached to \(B\), as shown in Figure 3. Initially \(P\) rests in equilibrium at the point \(O\), where \(A O B\) is a straight line.
- Find the length of \(A O\).
The particle \(P\) now receives an impulse of magnitude 6 N s acting in the direction \(O B\) and \(P\) starts to move towards \(B\).
- Show that \(P\) moves with simple harmonic motion about \(O\).
- Find the amplitude of the motion.
- Find the time taken by \(P\) to travel 1.2 m from \(O\).