A particle \(P\) moves on the \(x\)-axis with simple harmonic motion about the origin \(O\) as centre. When \(P\) is a distance 0.04 m from \(O\), its speed is \(0.2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the magnitude of its acceleration is \(1 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
Find the period of the motion.
The amplitude of the motion is \(a\) metres.
Find
the value of \(a\),
the total time, within one complete oscillation, for which the distance \(O P\) is greater than \(\frac { 1 } { 2 } a\) metres.