4. A particle moves with simple harmonic motion along a straight line. When the particle is 3 cm from its centre of motion it has a speed of \(8 \mathrm {~cm} \mathrm {~s} ^ { - 1 }\) and an acceleration of magnitude \(12 \mathrm {~cm} \mathrm {~s} ^ { - 2 }\).

1. Show that the period of the motion is \(\pi\) seconds.
2. Find the amplitude of the motion.
3. Hence, find the greatest speed of the particle.