Question 11 EITHER alternative.

A particle \(P\) of mass \(3 m\) is attached to one end of a light elastic spring of natural length \(a\) and modulus of elasticity \(k m g\). The other end of the spring is attached to a fixed point \(O\) on a smooth plane that is inclined to the horizontal at an angle \(\alpha\), where \(\sin \alpha=\frac{2}{3}\). The system rests in equilibrium with \(P\) on the plane at the point \(E\). The length of the spring in this position is \(\frac{5}{4} a\).
(i) Find the value of \(k\).

The particle \(P\) is now replaced by a particle \(Q\) of mass \(2 m\) and \(Q\) is released from rest at the point \(E\).
(ii) Show that, in the resulting motion, \(Q\) performs simple harmonic motion. State the centre and the period of the motion.

(iii) Find the least tension in the spring and the maximum acceleration of \(Q\) during the motion.