The disclosure provides a solution for monitoring stick-slip vibrations without using any surface torque measurements. Instead, the disclosure provides a method to monitor stick-slip vibrations based on rotational speed. A stick-slip monitor, a top drive controller and a method of operating a drill string are provided herein that use rotational speed for monitoring stick-slip vibrations. In one example, the method of operating a drill string includes: (1) performing a frequency domain analysis of an RPM signal associated with a top drive that is used to rotate a drill string, and (2) determining a presence of torsional oscillations of the drill string based on the frequency domain analysis of the RPM signal.