Forced Oscillation of a Spring-Mass System having Combined Coulomb and Viscous Damping

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Abstract
The solution for the response of a mass-excited dynamic system influenced by both coulomb and viscous damping has been previously presented. Although a direct mathematical analogy exists between the mass-excited and support-excited systems, there appears to be available no practical compilation of results for the support-excited system, interest which has been heightened by the demands of military installations of delicate electronic equipment. In the present paper, an analytic solution for the response of the support-excited system is presented. The solution to the equation of motion is developed through the application of a Fourier Series to represent the frictional force opposing the relative motion between mass and supporting structure. It is assumed that no stops occur during any portion of the steady-state oscillation. The results are presented in a form convenient for observing the influence of system parameters.