The problem with just animating the up/down motion is that it’s very difficult to sync everything together with the rotation like a merry-go round would:
each “horsey” goes up at the exact same position, even if it slows down or speeds up: they still go up at that position.
here’s a solution with expressions:
FreeVideoCoding.com
basically it uses the Y rotation of the parent null to calculate a sinusoidal up down in the Anchorpoint.
the Null has controls for:
“wobbles per revolution”, “amplitude”, “merry-go round radius”, and “N