Response of a simple system made complex by attaching subsystems—an analytic study.

A deceptively simple dynamical system comprised of a grounded mass to which are attached N, a large number, sprung masses has received much attention. The reported studies mostly involve physical experiments or numerical simulations. Given the large number of physical parameters needed to describe any single system, such a research agenda requires one to address an excessive number of experiment scenarios. Thus, the motivation for the analytical study reported. The focus of the study is the net force the attached subsystems cause to act on the base system. This force, while “internal” to the coupled system, is a response measure of primary importance since it accomplishes the work that determines the energy flow to and from the base system. As demonstrated, a further reason for the focus is an ability to construct an asymptotically valid, analytic expression for this response measure. Further demonstrated, using the constructed expression, is a resolution of a complex “process,” that describing the energy...