2 A particle \(P\) moves on a straight line \(A O B\) in simple harmonic motion. The centre of the motion is \(O\), and \(P\) is instantaneously at rest at \(A\) and \(B\). The point \(C\) is on the line \(A O B\), between \(A\) and \(O\), and \(C O = 10 \mathrm {~m}\). When \(P\) is at \(C\), the magnitude of its acceleration is \(0.625 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) and it is moving towards \(O\) with speed \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Find

1. the period of the motion, in terms of \(\pi\),
2. the amplitude of the motion. The point \(M\) is the mid-point of \(O B\). Find the time that \(P\) takes to travel directly from \(C\) to \(M\).