Generalized exact method of analysis of free and forced oscillations in the non-conservative physical system

In this paper, the fundamental problems in the generalized exact form used for the analysis of oscillations in composite physical systems, are presented. To these generalized problems belong such as: separation of variables in the complex Hilbert space, orthogonality of the eigenvectors of boundary-value problems, influence of the initial conditions and forced oscillations. The generalizations have been presented in the operator forms. In the case of real physical systems, it is necessary to transform the operator forms into suitable scalar ones. The presented approach is an essential extension of the method of separation of variable applied io the linear system of differential equations.