I'll take a shot
The magnetic attraction of the tube is equal along it's whole circumference, thus when the magnetized cylinder is dropped in, it's being pulled in every horizontal direction equally, so it's lodged perfectly in the middle while it falls.
>>#6, well, you know this guy already did his thing
also i was tired as **** when i wrote that. I meant the magnetic attractions are REPULSING it, not attracting.
>>#3, I like xxdarkdanxx's thinking, but that's not really there. I'll keep it simple:
The metal going down the tube is a conductor inducer. This means that the magnet makes a current in the copper tube, due to its magnetic property. According to Lenz's Law, "An induced electromotive force always gives rise to a current whose magnetic field opposes the original change in magnetic flux." This basically means that the magnetic property of the magnet in the middle makes a current, which causes the magnetic field of the copper tube to then turn and repel the magnet instead of attract it. Imagine the repelling force as something pushing against all sides of it. As gravity pulls it down and it is slightly pushed down by the repelling force, it slows down a lot until it escapes the opposite magnetic field.