2. A particle \(P\) is moving in a straight line with simple harmonic motion about the fixed point \(O\) as centre. When \(P\) is a distance 0.02 m from \(O\), the speed of \(P\) is \(0.3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the magnitude of the acceleration of \(P\) is \(0.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\)

1. Find the period of the motion. The amplitude of the motion is \(a\) metres. Find
2. the value of \(a\),
3. the total length of time during each complete oscillation for which \(P\) is within \(\frac { 1 } { 2 } a\)
   metres of \(O\). metres of \(O\).