6 A particle \(P\) of mass 0.1 kg moves in a straight line on a smooth horizontal surface. A force of \(( 0.36 - 0.144 x ) \mathrm { N }\) acts on \(P\) in the direction from \(O\) to \(P\), where \(x \mathrm {~m}\) is the displacement of \(P\) from a point \(O\) on the surface at time \(t \mathrm {~s}\).

1. By using the substitution \(x = y + 2.5\), or otherwise, show that \(P\) moves with simple harmonic motion of period 5.24 s , correct to 3 significant figures. The maximum value of \(x\) during the motion is 3 .
2. Write down the amplitude of \(P\) 's motion and find the two possible values of \(x\) for which \(P\) 's speed is \(0.48 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
3. On each of the first two occasions when \(P\) has speed \(0.48 \mathrm {~m} \mathrm {~s} ^ { - 1 } , P\) is moving towards \(O\). Find the time interval between
   (a) these first two occasions,
   (b) the second and third occasions when \(P\) has speed \(0.48 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).