Instruments and Systems: Monitoring, Control, and Diagnostics Annotation << Back Method of Acoustic Diagnostics of Supports Stiffness Elastically Coupled Shafts G.F .SAFINA Inverse spectral problem of diagnostics of stiffness coefficients of supports of elastically interconnected shafts by known values of frequencies of symmetrical oscillations of mechanical system is considered. The question of the existence and uniqueness of solving the problem of acoustic diagnostics was investigated. The corresponding theorems have been proved. To solve the problem, an additional parameter has been introduced. A method of solving the problem is presented, reduced to solving a system of algebraic equations with known values of three frequencies of symmetric vibrations of a system of connected shafts. Analytical formulas for the single recovery of the desired stiffness parameters are obtained. A numerical example of the application of the problem solving algorithm is given. Keywords: coupled shafts, acoustic diagnostics, frequency equation, stiffness of supports, frequency of oscillations, solution method. DOI: 10.25791/pribor.6.2022.1341 Pp. 10-14.