Dynamics of damped oscillations: physical pendulum

Abstract

The frictional force of the physical damped pendulum with the medium is usually assumed proportional to the pendulum velocity. In this work, we investigate how the pendulum motion will be affected when the drag force is modeled using power-laws bigger than the usual 1 or 2, and we will show that such assumption leads to contradictions with the experimental observation. For that, a more general model of a damped pendulum is introduced, assuming a power-law with integer exponents in the damping term of the equation of motion, and also in the nonharmonic regime. A Runge-Kutta solver is implemented to compute the numerical solutions for the first five powers, showing that the linear drag has the fastest decay to rest and that bigger exponents have long-time fluctuation around the equilibrium position, which have not correlation (as is expected) with experimental results.