The constants of equivalent systems without feedback for computing the responses of electromagnetic seismographs with several galvanometers

Summary

The amplitude and phase responses of electromagnetic seismographs with an arbitrary number of galvanometers, used to increase the dynamic range of the seismograph or to filter perturbing oscillations, are derived. The fundamental parameters of the system, i.e. the partial periods and the partial constants of damping of the seismometer and of the individual galvanometers, together with the coupling terms, are replaced by other constants. These enable the responses of each channel to be computed with the aid of a combination of elementary responses of the systems of the set with zero couplings between the galvanometers and a zero effect of the motion of the galvanometers on the motion of the seismometer. The elementary responses are defined by 2 types of substitute constants: equivalent constants, determined by the roots of the characteristic equation, or by the partial periods, and reduced damping constants. The possibilities of analysing a system with equivalent constants are demonstrated on the case of a seismograph with 2 galvanometers.