Jay, Gregory D., et al. Assuming Exponential Decay by Incorporating Viscous Damping Improves the Prediction of the Coefficient of Friction in Pendulum Tests of Whole Articular Joints. J Eng Med 221 PartH:325-333, 2007.
A pendulum test with a whole articular joint serving as the fulcrum is commonly used to measure the bulk coefficient of friction (COF). In such tests it is universally assumed that energy loss is due to frictional damping only, and accordingly the decay of pendulum amplitude is linear with time. The purpose of this work was to determine whether the measurement of the COF is improved when viscous damping and exponential decay of pendulum amplitude are incorporated into a lumped-parameter model.
It was found that the exponential decay function was able to predict the COF values within 2 percent error. This error increased for models in which the damping coefficient was relatively small and the COF was relatively large. On the other hand, the linear decay function resulted in large errors in the prediction of the COF, even for small values of viscous damping.