5. A particle \(P\) is moving in a straight line with simple harmonic motion on a smooth horizontal floor. The particle comes to instantaneous rest at points \(A\) and \(B\) where \(A B\) is 0.5 m . The mid-point of \(A B\) is \(O\). The mid-point of \(O A\) is \(C\). The mid-point of \(O B\) is \(D\). The particle takes 0.2 s to travel directly from \(C\) to \(D\). At time \(t = 0 , P\) is moving through \(O\) towards \(A\).

1. Show that the period of the motion is \(\frac { 6 } { 5 } \mathrm {~s}\).
2. Find the distance of \(P\) from \(B\) when \(t = 2 \mathrm {~s}\).
3. Find the maximum magnitude of the acceleration of \(P\).
4. Find the maximum speed of \(P\).