Combined viscous and dry friction damping of oscillatory motion

Abstract

The acceleration, velocity, and displacement of a glider on an air track undergoing oscillatory motion subject to viscous and dry frictional damping are investigated using an accelerometer, which allowed a detailed investigation of the dynamics, experimental observation of the predicted acceleration discontinuities due to the reversal of the friction force, and the variation of the drag with time, velocity, and displacement. The investigation included systematic variation of the air track air pressure to explicitly control the relative contribution of viscous and dry frictional damping. Although frictional damping of oscillatory motion has been treated by a number of authors, most investigations have been restricted to measurements of displacement only, with the primary interest being in the decay of the amplitude. In this paper, an exact theory of the acceleration of oscillatory motion, assuming viscous damping proportional to the velocity plus a Coulomb friction force independent of velocity or position, is presented and compared with experiment.