3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{9777abb8-a564-40d5-8d96-d5649913737b-08_307_437_244_756}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
A particle \(P\) of mass \(m\) is attached to one end of a light elastic spring of natural length \(l\) and modulus of elasticity \(k m g\), where \(k\) is a constant. The other end of the spring is fixed to horizontal ground.
The particle \(P\) rests in equilibrium, with the spring vertical, at the point \(E\).
The point \(E\) is at a height \(\frac { 3 } { 5 } l\) above the ground, as shown in Figure 1.
- Show that \(k = \frac { 5 } { 2 }\)
The particle \(P\) is now moved a distance \(\frac { 1 } { 4 } l\) vertically downwards from \(E\) and released from rest. Air resistance is modelled as being negligible.
- Show that \(P\) moves with simple harmonic motion.
- Find the speed of \(P\) as it passes through \(E\).
- Find the time from the instant \(P\) is released to the first instant it passes through \(E\).