B E.P.E. -> ? when 2 masses are attached to a spring

[Codemetry]

Two masses m and M are attached to a compressed spring. When the spring decompresses, the masses won't be pushed off the spring. What will happen to the masses and the entire system? By conservation of energy, the elastic potential energy of the spring will convert into kinetic energy, but which mass / entire system will have an increase in K.E.? What will happen to the center of mass?

 

[anuttarasammyak]

You should consider not only energy but momentum conservation. The center of mass keeps at rest. The masses oscillate around it.

 

[tech99]

I think it may be analogous to a capacitor with two inductors connected across it. This system has only one resonance, caused by the combined inductance. So the combined masses will determine the frequency, in combination with the spring stiffness. As the masses act in series, we need to find the effective total mass from 1/Mt = 1/M1 + 1/M2. The kinetic energy is entirely in the motion of the masses and would seem to be shared in inverse proportion to the masses.