I still find it fascinating that the slinky's bottom, essentially, doesn't start moving downward until the end. Even with a compressing center of mass, the slinky is so perfectly designed the energy in the tension equals the force of gravity.
The true explanation can only be found in God's humor.
thanks
I would say this differently: The slinky is a helical spring suspended from one end, so the tension force at any point along the spring is exactly what is necessary to support that part of the spring which is below that point.
In other words, it is not a coincidence that the force exactly balances gravity initially; it is the natural position of the spring, having the lowest potential energy.
It's fascinating to consider what would happen if a slinky were extended between two points along a horizontal friction-free surface, like an ice rink, and then one end of the slinky is released. My guess is that we would see a similar behavior, with the loose end collapsing toward the other end and a transition between collapsed coils and coils which are undisturbed from their initial positions.
Differently from the vertical case, the horizontal slinky would initially exhibit identical spacing between coils along its entire length.
We need somebody with a slinky, a high-speed camera, and an ice rink.