There is a'long history of research on pendulum systems, which has provided some striking discoveries, since it is simple to observe the phenomena in these widely occurring systems with their various properties, e.g., such systems were first used in observations on parametric resonance [ 11, 15] and high-frequency stabilization [2, 8]. Essentially novel features have been observed as regards states of chaos in pendulum systems [ 1, 5, 6, 13, 14]. The history of research on pendulum systems reflects advances in mathematics, mechanics, and physics. Here we consider the steady states in the resonant motion of a pendulum when the point of support is vibrated by a mechanism with restricted power, and also when chaos occurs in the interactions. Particular attention is given to how the source features affect the state. Deterministic chaos occurs [5, 6, 9] with a simple pendulum only if there is an external force, and extensive numerical data exist on the behavior of pendulums with inputs described by explicit time functions [6, 13]. However, if there is restricted excitation [3, 4], where the operation of the exciting device is dependent on the dynamic state, chaotic oscillations should give rise to analogous behavior, and consequently the system is subject to a chaotically varying input. One therefore has to consider how the individual features of the device affect the oscillations. Before deterministic chaos was discovered, a reduction principle was used in researching complex systems: the system was split up into parts, each examined separately. The recognition of chaotic states led to the view that the combined system may have fairly complicated behavior because of the interaction between several components [7], so one anticipates that a pendulum acted on by a restricted force will show behavior that gives much more information on the interaction rather than the properties of the pendulum. Here one cannot neglect the coupling of the pendulum to the mechanism on the argument that it is weak (which is mathematically expressed as small terms describing it) because even a weak interaction produces an essentially different motion pattern. We consider the Fig. 1 system. The crank mechanism is coupled via the rod b to the support of a physical pendulum. When the drive a rotates through an angle O, the slider together with the suspension shows a displacement u(t) = altos O + (al/4)(1 + cos 20)], in which a i ffi a/b. An Oxz cartesian coordinate system is used to describe the pendulum oscillations, and the kinetic energy of the entire system, with the mass of the slider taken as negligible, is [3, 12, 13]