Parabolic dish ellipse oscill

(source Description: The animation shows a rotating parabolic dish. On the left the motion as seen from an inertial point of view, on the right the motion as seen from a co-rotating point of view. The dish is solid and it has exactly the same shape as a fluid rotating at that angular velocity has. The dark dot is a puck that can slide over the surface with very little friction. The parabolic dish is very shallow: the up-down motion of the puck is very small compared to the motion parallel to the dish's surface.

Since the force towards the center is proportional to the distance to the center, the shape of the trajectory of the puck is an ellipse. This ellipse can be thought of as two perpendicular harmonic oscillations. As seen from a rotating point of view only the eccentricity of the ellipse-shaped trajectory is visible.

The eccentricity can be thought of as a combination of two oscillations: an oscillation of the angular velocity and an oscillation in the distance to the center of rotation.