Oscillations with three damping effects

Abstract

Experiments on oscillatory motion are described with three different damping effects. The first experiment is a physical pendulum whose damping mechanism is due to sliding friction; the second is magnetic resistance due to eddy currents; and the third experiment involves a pendulum setup where air resistance is the dominant factor. These three damping mechanisms yield constant (/||), linear, and quadratic resistances in velocity respectively. Approximation methods are described for treating the three damping effects and a general solution is derived for the damping with a very general velocity dependence. A sonic rangefinder is used to record the oscillatory motions of the pendulums. The experimental measurements and theoretical calculations are in a good agreement.