2 A particle \(P\) moves on a straight line in simple harmonic motion. The centre of the motion is \(O\), and the amplitude of the motion is 2.5 m . The points \(L\) and \(M\) are on the line, on opposite sides of \(O\), with \(O L = 1.5 \mathrm {~m}\). The magnitudes of the accelerations of \(P\) at \(L\) and at \(M\) are in the ratio 3:4.

1. Find the distance \(O M\).
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   The time taken by \(P\) to travel directly from \(L\) to \(M\) is 2 s .
2. Find the period of the motion.
3. Find the speed of \(P\) when it passes through \(L\).