Another motorized variant of Tulio Laanens fabulous Marble Machine #3. A video is here: https://www.youtube.com/watch?v=qM1W1ws6z9Q
This is for an inexpensive pancake style geared synchronous AC motor with 7mm shaft with a flat. These are available in various voltages and RPM ratings. For safety, I suggest you use a low voltage AC wall wart (e.g. 12V AC) and select a motor accordingly. The base has a hole that fits a standard panel mount DC connector, which needs a 10.9mm hole. The motors are available with different gearing which of course will dictate the feed rate. I selected 30 RPM, but you can definitely go slower if you like, and possibly even faster, although I did not try that. The motor must be CW rotation. I bought mine here: http://www.ebay.com/itm/AC5V-6V-9V-12V-24V-110V-220V-TYC-Plastic-Gear-Synchronous-Reduction-Gear-Motor-S/231968344955
If you have already made the track, you do not have to reprint. You can modify it for motorization simply by drilling a 10mm hole in the middle of the bottom plate. I suggest you print a new spiral, however. There are 3 variants with different tolerances for the motor axle press fit. I suggest you start with the middle one.
I have also made a new top without the finger hole, but this is not a necessity.