The work performed was focused on the study of a gyroscopic vertical rotor supported at its lower end by a hinge joint, at its upper end, closer to the rotor disk by a viscoelastic support and above the disk connected to the fixed part by means of a shear magnetic bearing. The mount consists of two permanent magnets, one of which is attached to the fixed part and the other to the rotor disc. The magnets attract each other, which always returns the rotor to the equilibrium position during its vibration. In the developed calculation technique, permanent magnets are represented by electric coils powered by an equivalent current. Assuming that the radii of the turns are significantly smaller than the distance between them, the attractive force of the fixed current turn of the movable current turn is determined, the equations of motion of the gyroscopic rotor system are formulated. The amplitude characteristic shows that the use of the proposed magnetic bearing reduces the vibration amplitude of the rotor in the region to a critical speed, shifts the critical speed towards its increase. Involving the nonlinear stiffness of the support material when interacting with linear and cubical nonlinear damping transfers the vibration insulation properties of the magnetic bearing attractive forces from the region of less than the critical value of the shaft rotation speeds to the region near the resonant speed. This allows us to develop a new, more efficient combined damping method, a method for controlling resonant amplitudes for smooth resonant passages, and expand the range of operating speeds.