Two blocks A and B each of mass m are connected by a massless spring of natural length L and spring constant k. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in figure. A third identical block C, also of mass m, moves on the floor with a speed v along the line joining A to B and collides with A. Then

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Here, at maximum compression xmax, we introduce the concept of reduced mass μ of the system (details$$ discussed in Rotational $$Dynamics).        $$1$$μ$$=1m+1m$$⇒ μ$$=m2Further$$, by Law of Conservation of Energy       $$12$$μ$$v2=12kxmax2$$⇒ $$xmax=vm2k$$ and          $$KE$$$$=12$$μ$$v2=12m2v2$$⇒ $$KE$$$$=mv24$$

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