Time-periodic modulation of a mechanical system parameters may lead to resonances, instabilities and some pattern formation. This paper deals with an approximative solution in the analytical form of some second order linear differential equation with time depend parameters. The analytic solution is compared with the numerical solution obtained by the Runge-Kutta method and the conditions of the convergence of this analytical method are discussed.

This work is supported by KEGA 015ŽU-4/2017 Digital technologies for machine building study programs as a part of strategy "Internet of Things".