Asymptotic analysis of kinematically excited dynamical systems near resonances

The dynamic response of a harmonically and kinematically excited spring pendulum is studied. This system is a multi-degree-of-freedom system and is considered as a good example for several engineering applications. The multiple-scale (MS) method allows us to analytically solve the equations of motion and recognize resonances. Also stability of the steady-state solutions can be verified. The transfer of energy from one to another mode of vibrations is illustrated.