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What is the velocity of the smaller mass and of the larger mass when the spring is maximally compressed?

What is the maximum compression of the spring?

Solve in terms of the variables; the surface is frictionless.

What I did was assume both springs have 0 velocity at maximal compression, and just solved for the compression by equating the elastic potential energy with the kinetic energy of the masses the instant after impact. I know my assumption is very unsound.

What's the proper way to solve this?