4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{45c51316-7d58-4c16-9b5f-1d7421060a88-4_332_1056_251_459}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{figure}
A small smooth bead \(B\) of mass 0.2 kg is threaded on a smooth horizontal wire. The point \(A\) is on the same horizontal level as the wire and at a perpendicular distance \(d\) from the wire. The point \(O\) is the point on the wire nearest to \(A\), as shown in Fig. 2. The bead experiences a force of magnitude \(5 ( A B )\) newtons in the direction \(B A\) towards \(A\). Initially \(B\) is at rest with \(O B = 2 \mathrm {~m}\).
- Prove that \(B\) moves with simple harmonic motion about \(O\), with period \(\frac { 2 \pi } { 5 } \mathrm {~s}\).
- Find the greatest speed of \(B\) in the motion.
- Find the time when \(B\) has first moved a distance 3 m from its initial position.