6 A particle \(P\) starts from rest at a point \(A\) and moves in a straight line with simple harmonic motion. At time \(t \mathrm {~s}\) after the motion starts, \(P\) 's displacement from a point \(O\) on the line is \(x \mathrm {~m}\) towards \(A\). The particle \(P\) returns to \(A\) for the first time when \(t = 0.4 \pi\). The maximum speed of \(P\) is \(4 \mathrm {~ms} ^ { - 1 }\) and occurs when \(P\) passes through \(O\).

1. Find the distance \(O A\).
2. Find the value of \(x\) and the velocity of \(P\) when \(t = 1\).
3. Find the number of occasions in the interval \(0 < t < 1\) at which \(P\) 's speed is the same as that when \(t = 1\), and find the corresponding values of \(x\) and \(t\).