I came across this on a Radio Lab podcast.
they talked of the top communicating to the bottom, and that the reason that the bottom doesn't fall, is that it doesn't know the top was released.
I'm not going to say that's a silly way to look at it, as I don't quite get it.I mean, i kind of get it. At the bottom, the spring is still stretched out, so there is still the tension there, and if nothing about the tension has changed, why would the bottom fall? But it seems like an unusual way of explaining it compared to what I'm familiar with.
Can't it also be explained in terms of the center of mass? As in, shouldn't the center of mass be falling at normal acceleration due to gravity? And because of the tension in the spring the center of mass is changing its position relative to the length of the spring. Meaning the top of the spring has tension on it, so it falls faster than the center of mass. the bottom has tension on it, pulling up, so it falls slower than the center of mass.
I am not good with differential equations, but i imagine one would be needed to model the way a point on the slinky falls.