In the article, it is shown that the implementation of the inertial element in the form of four cross-shaped magnetic conducting sectors with permanent magnets installed in them, the poles of which alternate in adjacent sectors, the placement of the measuring windings on the pole tips of the magnetic conductor, located coaxially with the corresponding sectors of the inertial element, the implementation of the mass of two adjacent sectors of the inertial element, exceeding the mass of the other two adjacent sectors provides the measurement of linear vibration oscillations in all three mutual components of the transducer. It is established that in the investigated transducers, the transient characteristic consists of two free (oscillatory and aperiodic) components and one forced component. Forced oscillations occur with the frequency of the input perturbing force; the amplitude of forced oscillations does not depend on the initial conditions and time, and in forced oscillations with damping, there is always a shift of the oscillation phase compared to the phase of the input perturbing force. It is revealed that the attenuation rate of the free oscillatory component depends on the attenuation coefficient of the mechanical circuit, and the aperiodic component depends on the time constant of the measuring circuit of the transducer. In the structural schemes of automatic control systems, the investigated transducers are represented as a series of connected oscillating, ideal differentiating links and an inertial link of the first order.