Mechanical resonance in the rear wheels of a shopping trolley

A mechanical resonance phenomenon in the rear wheels of a common shopping trolley is investigated. The trolley examined in this paper has the rear wheels attached to long beams, with no horizontal bar connecting the beams. The beams are thus free to vibrate along their entire lengths. In a resonant mode the beams vibrate with a small amplitude in a direction perpendicular to the general motion of the trolley and the wheels, attached to the beams by ball bearings, vibrate around a vertical axis, with an amplitude of several degrees. The trolley may enter the resonance if the rear wheels hit a small object, e.g. a grain of gravel, or if one of the wheels is tapped when the loaded trolley is in motion. The resonance is stable and lasts until the trolley is slowed down enough, or stopped. The resonance mode is modeled analytically and the resulting differential equations are solved numerically. Comparison is made to experimental data obtained using a high-speed video camera. (paper)