We consider a model of damped vibrations based on fractional differentiation. The model given is completely consistent with the classical model of vibration with viscous damping. We find the relation between the order of fractional differentiation in the equation of motion and Q-factor of an oscillator. The proposed approach seems more appropriate for the physical nature of the described system. The experiment with a vibrating piezoelectric plate, performed as part of the study, showed good agreement with the model and confirmed that the fractional oscillator model can be used to describe strongly damped vibrations.

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