Solid Body Rotation Vibration

For solid body rotation of an incompressible fluid inside a vertical cylinder (open to air at the top with gravity acting down) it is proposed that if a small piece of fluid is displaced horizontally and radially by a short distance and then released, it will oscillate with a constant frequency as viewed in the rotating frame of reference. The oscillation frequency is derived to be equal to the basic frequency of the solid body rotation. Also it is hypothesized that a wave type of motion of the solid body rotation should be possible at the air/fluid interface. Experimental verification is needed for the conjectured vibration and wave motion of the solid body rotation.