I think slinky springs are great. The slow motion videos of the slinky are just cool. I also love the fact that towards the end, they interview the guy with the computer model of the slinky spring, and it is just transparent that he loves working out what is happening, just for its own sake. Thanks to @RHULPhysics for the tweet with the link.

I think we can understand the apparently odd observation that the bottom of the spring  does not move, with only the formula for harmonic motion. By this I mean that we can see that two timescales are about the same. The first timescale is the time for the bottom of the slinky to realise that top has been let go. The second timescale is the time for the centre of mass of the slinky spring to fall from its initial position in the middle of the stretched slinky to bottom of the spring.

We can do this just using the basic expression for the timescale of harmonic motion, τ, τ = √(m/k), where m is the mass and k is the spring constant. This is the basic timescale over which the spring shrinks or stretches.

The mass of a biggish slinky spring is I guess about 1 kg. Now a Newton is about the weight of 1 apple. I estimate that if you take an apple and attach it to the slinky spring, the spring will get maybe 10 cm longer. This gives me a spring constant of 1 N/ (0.10 m) = 10 N/m.

So the time between the top being let go and the bottom of the spring realising this is around τ = √(m/k) =  √(1/10), or about 0.3 s. This is short and so hard to see with the naked eye, but if you use a fast camera and slow up the images, you see everything beautifully.

Also, if the slinky spring’s centre of mass is 1 m off the ground, it will take almost √(2× 1 m /10 m/s²) = 0.4 s to hit the ground [taking the acceleration due to gravity g = 10 m/s²]. So the time to hit the ground, and the time for the bottom of the spring to realise that the top has been let go are very close, which is what you can see in the movies. I like it when physics works like this.