Centre of mass, collision, momentum

[karanbir]

Two blocks m1 and m2 are connected by an ideal spring of force constant k. The blocks are placed on smooth horizontal surface. A horizontal force F acts on the block m1. Initially spring is relaxed, both the blocks are at rest.
What is maximum elongation of spring?

i think it would be when both the objects are moving with same velocity, so i applied law of conservation of energy but the equation has too many variables.

 

[haruspex]

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