The harmonic response and resonance frequency behavior of the spring supported FGM beam against the lateral motion for the various values of support stiffness at the ends are analyzed by using the force transmissibility parameter with the finite-element method and Lagrange's equations. The steady-state responses to a sinusoidal varying force are determined for the support reactions in a frequency domain. The problem is solved within the framework of the Timoshenko beam theory. For the convergence study, some of the results are compared with previous works' values, and a good agreement can be seen. The study concludes that the support stiffness, volume fraction coefficient and the ratio of young module level all strongly affect the natural frequencies and the force transmissibility. For some values of spring stiffness of support, the rigid body motion of the beam occurs and reduces the effect of volume fraction coefficient on the natural frequencies.