We study a mathematical model of systems of controlled machine units with distributed and discrete parameters. The method is based on a non-conservative boundary value problem with complicated boundary conditions. We develop a method of determination of complex-valued eigenvalues for the given class of non-conservative problems, which is based on the method of normal fundamental systems of solutions. In result of calculations performed under specific values of parameters of the systems, we plot the graphics of real and imaginary parts of the first two complex eigenvalues versus a dimensionless parameter proportional to the stiffness parameter of the motor. We also determine the conditions under which the oscillations of different character, including self-exciting oscillations, take place. We demonstrate that varying the eigenvalues, we can avoid unwanted oscillations which correspond to different types of feed back forces. The examples of systems of machine units are considered. We show that the effect of ratios of distributed and discrete parameters on the character of possible oscillations can be accounted for while the system designing.