This demostration covers the center of mass motion of a system of particles. The system, in this case, is compsed of three carts. Two identicle carts connected by a rigid rod flank a third more massive cart which is connected by a spring to the right hand cart as shown in the picture below. The arrow in the picture indicates the location of the center of mass of the system at rest.
Newton's second law for a system of particles states that in the absence of a net external force, there is no acceleration (change of motion) of the center of mass. However, the particles(carts) themselves may still move around as long as the center of mass does not change.
The spring is stretched and then released. The instant after it is released, there are no external forces on the system of carts. (The spring creates an internal force.) Then, according to Newton's second law, the center of mass should remain constant.
In the movie, an arrow depicts the center of mass. It can be seen that as the inner cart moves in one direction, the outer carts move in the opposite direction which keeps the center of mass at the point depicted by the arrow.
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