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.
(i) Find the distance \(O M\).

The time taken by \(P\) to travel directly from \(L\) to \(M\) is 2 s .
(ii) Find the period of the motion.

(iii) Find the speed of \(P\) when it passes through \(L\).