2 A particle \(P\) moves on a straight line in simple harmonic motion. The centre of the motion is \(O\). The points \(A\) and \(B\) are on the line on opposite sides of \(O\) such that \(O A = 3.5 \mathrm {~m}\) and \(O B = 1 \mathrm {~m}\). The speed of \(P\) when it is at \(B\) is twice its speed when it is at \(A\). The maximum acceleration of \(P\) is \(1 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).

1. Find the speed of \(P\) when it is at \(O\).
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2. Find the time taken by \(P\) to travel directly from \(A\) to \(B\).