This paper concentrates on the vibrations attenuation of a rotor driven by a DC motor and its frame flexibly coupled with a baseplate by linear cylindrical helical springs and damped by an element that can work either in inertia or impact regime. The system oscillation is governed by three mutually coupled second-order ordinary differential equations. The nonlinear behaviour occurs if the impact regime is adjusted. The damping element operating in inertia mode reduces efficiently the oscillations amplitude only in a narrow frequency interval. In contrast, the damping device working in impact regime attenuates vibrations of the rotor frame in a wider range of the excitation frequencies and it can be easily extended if the clearances between the rotor casing and the damping element are controlled. The development of a computational procedure for investigation of vibration of a flexibly supported rotor and for its attenuation by the inertia and impact dampers; learning more on efficiency of the individual damping regimes; finding possibilities of extension of the frequency intervals of applicability of the damping device; and obtaining more information on the character of the vibration induced by impacts are the main contributions of this research work.