This is fascinating to see. I'd love to sit down and think through the impact of the discontinuous spring constant and energy loss - the relaxed state of the slinky is collapsed, with all the coils in contact, so it can't really oscillate about a neutral position. If you just let the bottom of the slinky sit on the floor, holding the top above, and drop it, it doesn't bounce back to the height you let it go; it hardly bounces back at all - a lot of the potential energy and deformation energy are getting lost. If you took a more "physics-y" spring, you could superimpose the oscillatory motion of any point on the spring with the rigid body motion under gravity. Although you couldn't treat the mass of the spring as negligible in the oscillatory solution like you would with a more traditional spring/mass problem....
This is fascinating to see. I'd love to sit down and think through the impact of the discontinuous spring constant and energy loss - the relaxed state of the slinky is collapsed, with all the coils in contact, so it can't really oscillate about a neutral position. If you just let the bottom of the slinky sit on the floor, holding the top above, and drop it, it doesn't bounce back to the height you let it go; it hardly bounces back at all - a lot of the potential energy and deformation energy are getting lost. If you took a more "physics-y" spring, you could superimpose the oscillatory motion of any point on the spring with the rigid body motion under gravity. Although you couldn't treat the mass of the spring as negligible in the oscillatory solution like you would with a more traditional spring/mass problem....
Oooh, that might be a thing to look at-- replacing the slinky with a bunch of stiffer springs and seeing if that changes the dynamics...
It's too bad I have to work today.