Create a plastic track, shaped like an inverted cycloid.
Place in this track a steel ball bearing.
Add a c-shaped electromagnet around the center of the
track, so that they can magnetically attract or repel the
ball when energized.
Add a sensor in the middle of the track; also, add two
one on either side of the first on, and both
equidistant from it.
Add some electronics and a voltage source, so that the
electromagnet get energized when the ball triggers the
left or right sensor twice in a row. When the center
is triggered, the the electromagnet is turned off.
Each time the rolling magnet passes through the center,
the electromagnet briefly pulls the ball, adding
to it's speed.
If the ball were sliding frictionlessly, then it's period
depend solely on the radius of the cycloid; I honestly
know how much effect there is due to the moment of
Since there's friction involved, the ball shouldn't go flying
off the top edge of the track if you use a reasonably
On the other hand, if the voltage *is* high enough to lift
the ball all the way past the top, then this could be used
a lift for a rolling ball kinetic sculpture. In this case, the
track doesn't need to be cycloid shaped; a parabola, or a
shape, or some odd 3-D shape, etc, will work... so long
the ball doesn't lose too much kinetic energy going back