A frequency equation of a Timoshenko beam carrying a two-degree of freedom spring-mass system

In paper construct a frequency equation for a mechanical system that consist of a rigid two degree of freedom mass that was attached by two springs to the Timoshenko beam. The system that we considered described a hybrid system of differential equations that with help a harmonic substitute transform into an algebraic-differential system relatively amplitude parameters. The frequency equation was obtained by review of conditions of the solution existence of the boundary problem for the algebraic differential equation.