The aim of the present paper is to study virtual steady-state vibrations in the neighbourhood of resonance conditions of a rotor with six degrees of freedom in linear homogeneous elasto-viscous field. Unstable frequencies zones are determined by "limited" power of an electric motor with linear characteristic and only one time-constant. Bogoliubov Mitropolsky's asymptotical method is applied in the neighbourhood of single basic resonance by small difference between natural and driving frequencies. The influence of the motor's time-constant is analyzed on the value of unstable frequency's zones by quasi steady-state increasing/decreasing frequencies (jump phenomenon). By special condition increasing of the driving frequency in growing rate could be seen right after resonance due to transfer from "small" angular coordinates to main rotation. Experimental result is applied.