- A particle \(P\) moves in a straight line with simple harmonic motion about a fixed point \(O\). The magnitude of the greatest acceleration of \(P\) is \(18 \mathrm {~m} \mathrm {~s} ^ { - 2 }\)
When \(P\) is 0.3 m from \(O\), the speed of \(P\) is \(2.4 \mathrm {~ms} ^ { - 1 }\)
The amplitude of the motion is \(a\) metres.
- Show that \(a = 0.5\)
- Find the greatest speed of \(P\).
During one oscillation, the speed of \(P\) is at least \(2 \mathrm {~ms} ^ { - 1 }\) for \(S\) seconds.
- Find the value of \(S\).