3 A particle Q is performing simple harmonic motion in a vertical line. Its height, \(x\) metres, above a fixed level at time \(t\) seconds is given by $$x = c + A \cos ( \omega t - \phi )$$ where \(c , A , \omega\) and \(\phi\) are constants.

1. Show that \(\ddot { x } = - \omega ^ { 2 } ( x - c )\). Fig. 3 shows the displacement-time graph of Q for \(0 \leqslant t \leqslant 14\). \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{86dd0c01-970d-4b67-9a6c-5df276a4a2be-4_547_1079_703_495} \captionsetup{labelformat=empty} \caption{Fig. 3}
   \end{figure}
2. Find exact values for \(c , A , \omega\) and \(\phi\).
3. Find the maximum speed of Q .
4. Find the height and the velocity of Q when \(t = 0\).
5. Find the distance travelled by Q between \(t = 0\) and \(t = 14\).