How do rocking horses work?
The center of mass of the horse and rider has to be below the center of curvature of the rockers for the horse to be stable (return to the upright position when the rider sits still). This constraint means that the rider physically rises a little when the horse is not in its centered position, and falls back to the lowest height when the horse is at center position. This rise and fall is what gives the horse its stability. The ratio between center of mass height and center of curvature height sets the natural resonant frequency of the ride. The closer these two are, the slower the natural rocking frequency. If the center of gravity is higher than the center of rocker curvature, then the horse is unstable and will fall over.
