A system for damping at least one resonant mode of a rotor drive train of an engine having a generator comprising a free turbine, the at least one resonant mode occurring at at least one resonant frequency, the system comprising: a filtering unit configured to receive a speed signal indicative of a present measurement of a speed of rotation of the free turbine and containing the at least one resonant frequency and a plurality of contributing frequencies, characterized by: the filtering unit being configured to decouple the speed signal into a resonant signal and a resonant-free signal, by attenuating the contributing frequencies to generate from the speed signal the resonant signal containing the at least one resonant frequency and the attenuated contributing frequencies, and attenuating the at least one resonant frequency to generate from the speed signal the resonant-free signal containing the plurality of contributing frequencies and the attenuated at least one resonant frequency; and a compensator unit coupled to the filtering unit and configured to receive the resonant signal and estimate therefrom a derivative of the speed signal and to generate from the derivative a damping signal indicative of a request to adjust a speed of the generator for damping the at least one resonant mode. a filtering unit configured to receive a speed signal indicative of a present measurement of a speed of rotation of the free turbine and containing the at least one resonant frequency and a plurality of contributing frequencies, characterized by: the filtering unit being configured to decouple the speed signal into a resonant signal and a resonant-free signal, by attenuating the contributing frequencies to generate from the speed signal the resonant signal containing the at least one resonant frequency and the attenuated contributing frequencies, and attenuating the at least one resonant frequency to generate from the speed signal the resonant-free signal containing the plurality of contributing frequencies and the attenuated at least one resonant frequency; and a compensator unit coupled to the filtering unit and configured to receive the resonant signal and estimate therefrom a derivative of the speed signal and to generate from the derivative a damping signal indicative of a request to adjust a speed of the generator for damping the at least one resonant mode. the filtering unit being configured to decouple the speed signal into a resonant signal and a resonant-free signal, by attenuating the contributing frequencies to generate from the speed signal the resonant signal containing the at least one resonant frequency and the attenuated contributing frequencies, and attenuating the at least one resonant frequency to generate from the speed signal the resonant-free signal containing the plurality of contributing frequencies and the attenuated at least one resonant frequency; and a compensator unit coupled to the filtering unit and configured to receive the resonant signal and estimate therefrom a derivative of the speed signal and to generate from the derivative a damping signal indicative of a request to adjust a speed of the generator for damping the at least one resonant mode.