An experimental impact oscillator

Abstract

The present work considers the impacting behavior of a piecewise linear experimental system, a previous version of which has successfully displayed a wide variety of non-linear, including chaotic, behavior in other previous experiments [1–3]; making use of the ‘ball rolling on a hill’ concept, a cart is constrained to roll along an ‘energy well’ track, shaped in the form of a parabola such that the governing equations of motion of the cart are almost linear. In contrast to previous studies, where the impact condition was fixed (usually at equilibrium), the rigid barrier is placed at varying positions along the track in this study to provide a displacement constraint that gives rise to a discontinuity in the restoring force on the cart (provided solely by gravity in the non-impacting region). Varying the position of the impact can significantly change the overall behavior of the system, and this experimental study will concentrate on behavior where the impact point is varied among three different positions along the parabolic track, one chosen at a position less than equilibrium, one chosen at equilibrium, and one chosen greater than equilibrium; wide and varied responses are observed for these cases. Data were collected with the LabVIEW object-oriented, programmable interface, about which a few salient features are also discussed.