Harmonic Oscillation in the Presence of Multiple Damping Forces

The relatively mundane damped harmonic oscillator is found to exhibit interesting motion once under the influence of both a velocity dependent and a Coulombic frictional damping force. Data for the decay of the amplitude as a function of time were collected on a specially prepared torsional oscillator. with a variable electromagnetic damping mechanism. An analytical solution of the appropriate equation of motion was obtained by the method of Laplace transforms. In both the limits of zero Coulombic friction and zero velocity damping, the solution reduces to the well-known answers to the problem. the solution, when plotted with the correct parameters, fits the numerical solution very well. The solution also shows excellent quantitative agreement with the experimental data