Speed of two blocks connected by a spring and velocity of its center of mass

Question

In the following short of the MIT regarding two blocks connected by a spring, it can be seen that the center of mass of the two-block system moves at constant velocity.

However, in a side question: "What is the speed of the blocks at the instant when the spring is at maximum compression?" the provided answer confuses me: "When the spring is at maximum compression both blocks are momentarily at rest relative to each other but they are still translating to the right with the velocity of the center of mass"

I can see that one block stops momentarily relative to me (as in, I hide with my hand the left block and the spring, and the block moves, and stops, moves, and stops).

How can be said that its velocity is the constant velocity of the center of mass at that point if the block stops momentarily at that instant?

Answer 1

You are confusing two moments in time here. One is the instant the spring is maximally compressed, the other is when one of the blocks is (almost) at rest relative to the rail (ground). These are not occuring at the same time, but it is difficult to see because you need to pay precise attention to two quantities at the same time (spring compression and block velocity).

Let's focus on the block in front (on the right). It moves to the right, then decelerates to a stop, and accelerates again. The important point is that, as soon as the spring is shorter than its rest length (it is compressed), the right block is already accelerating (way before the spring is maximally compressed), so by the time of maximum spring compression, the front block is no longer at rest, but has been accelerated to the speed the center of mass is always moving in (because at that instant there is no relative motion of the blocks).