Collision in Spring-mass System-1!

Two bodies \(A\) and \(B\) of mass \(m\) and \(2m\) respectively are placed on a smooth floor. They are connected by a spring of negligible mass. A third body \(C\) of mass \(m\) is placed on the floor. The body \(C\) moves with a velocity \(v_0\) along the line joining \(A\) and \(B\) and collides elastically with \(A\). At a certain time after the collision it is found that the instantaneous velocities of \(A\) and \(B\) are same and the compression of the spring is \(x_0\). The spring constant \(k\) will be :

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