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This paper describes frequency entrainment in self-excited oscillators which are mechanical vibration systems controlled by velocity feedback with variable gain. The oscillators are in a state of self-excitation, or in a state of vibration suppression by velocity feedback gain. When external force to the oscillator is small, the velocity feedback has a positive gain and self-excited vibration is generated. When external force is large and the vibration amplitude of the oscillator reaches the reference only by forced vibration, velocity feedback suppresses vibration actively, and then frequency entrainment occurs (forced entrainment). The synchronization limit of forced entrainment is derived from the resonance curve of forced vibration. Frequency entrainment in the plural oscillators (mutual entrainment) can be treated as force entrainment by substituting external force for the interaction of the other oscillator.

Frequency Entrainment in Self-Excited Oscillators Controlled by Velocity Feedback with Variable Gain