Question

Two masses m and 2m are connected by a spring and rest on a horizontal table on which friction can be neglected. The two masses are pulled apart to a length L and released from rest. Describe 

(a) the location of the center of mass before the masses are released, and 

(b) the motion of the center of mass after the masses are released from rest. 

Answer 1

The center of mass will be located closer to the greater mass. In fact, the center of mass will be located at a distance of 1/3L from 2m and 2/3L  from m. 

(b) Before the masses are released, the center of mass is at rest. After the masses are released, there are no external forces acting on the center of mass, and therefore the momentum of the center of mass does not change, remaining at rest while the two masses oscillate about it. It also follows that the momentum of block m is equal and opposite to block 2m at all times during the oscillation of the masses.