Torsional vibrations in a rotating structure having a relatively large mass and subject to varying frequencies of torsional excitation are damped by determining the frequency of torsional excitation of the rotating structure and coupling to the rotating structure a damping pendulum of smaller mass to provide an absorber unit rotating therewith. The angular displacement of the damping pendulum relative to the rotating structure is continuously monitored, and the frequency of excitation is determined. The monitored displacement of the damping pendulum together with the mass damper characteristics of the absorber unit are processed to output a signal which produces a control torque on the damping pendulum proportional to the monitored displacement of the damping pendulum with a controlled time delay to produce control torque on the damping pendulum substantially equal to the torsional excitation of the rotating structure. This produces resonance of the damping pendulum substantially at the torsional excitation of the rotating structure which is effective to damp the vibrations of the rotating structure.
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