This monograph deals with two important dynamic systems design problems: how to isolate elastically supported bodies from the effects of externally applied periodic excitation and determining equivalent static design loads for bodies that undergo sudden impact. The model used to investigate the isolation issue is a single degree of freedom system consisting of a mass connected by a linear weightless spring to a fixed base subjected to harmonic inputs. Two limiting cases are examined to address the issue of sudden impact. One model consists of elastic bodies that separate following collision with no loss of energy. The second model consists of inelastic bodies that remain fixed to one another following collision and energy is dissipated.