If I am right, then the slinky basically pancakes from top to bottom. So imagine that initially the top is at h=1 and the bottom at h=0. At some point, the top x units have collapsed, but the bottom 1-x are still standing. So the center of mass is x(1-x) + (1-x)(1-x)/2. But since the slinky is in freefall, the center of mass, as a function of time, is 1/2 – 1/2 g t^2.

Set them equal, solve and get x = sqrt(g) t, valid until t = 1 / sqrt(g) and x=1. So I think that’s why the top falls at constant speed.

What do you think?

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