6 A particle \(P\) starts from rest from a point \(A\) and moves in a straight line with simple harmonic motion about a point \(O\). At time \(t\) seconds after the motion starts the displacement of \(P\) from \(O\) is \(x \mathrm {~m}\) towards \(A\). The particle \(P\) is next at rest when \(t = 0.25 \pi\) having travelled a distance of 1.2 m .

1. Find the maximum velocity of \(P\).
2. Find the value of \(x\) and the velocity of \(P\) when \(t = 0.7\).
3. Find the other values of \(t\), for \(0 < t < 1\), at which \(P\) 's speed is the same as when \(t = 0.7\). Find also the corresponding values of \(x\).