Three uniform small spheres \(A, B\) and \(C\) have equal radii and masses \(3 m, m\) and \(m\) respectively. The spheres are at rest in a straight line on a smooth horizontal surface, with \(B\) between \(A\) and \(C\). The coefficient of restitution between each pair of spheres is \(e\). Sphere \(A\) is projected directly towards \(B\) with speed \(u\).
(i) Find, in terms of \(u\) and \(e\), expressions for the speeds of \(A, B\) and \(C\) after the first two collisions.
(ii) Given that \(A\) and \(C\) are moving with equal speeds after these two collisions, find the value of \(e\).