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 \(1 \mathrm{~m} \mathrm{~s}^{-2}\).
(i) Find the speed of \(P\) when it is at \(O\).

(ii) Find the time taken by \(P\) to travel directly from \(A\) to \(B\).