hi jimi70

The heavier weight (W) is dragging the lighter one (L). When W hits the floor, L is going up with the same velocity. W cannot go any further but L can, so the string goes slack. Let's call that point for L, the point X.

Now, L can go up for a while under gravity; it slows, stops and starts back down. All this time the string is slack. But when L gets back to point X the string is back to where it was. L is going down; the distance from L measured up to the peg and down again towards W is equal to the length of the string. So, at that moment the string is taut again.

Bob