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 \(O\), with \(O A = 1.6 \mathrm {~m}\) and \(O B = 1.2 \mathrm {~m}\). The ratio of the speed of \(P\) at \(A\) to its speed at \(B\) is \(3 : 4\).
- Find the amplitude of the motion.
The maximum speed of \(P\) during its motion is \(\frac { 1 } { 3 } \pi \mathrm {~m} \mathrm {~s} ^ { - 1 }\). - Find the period of the motion.
- Find the time taken for \(P\) to travel directly from \(A\) to \(B\).