Dynamics of damped oscillations: physical pendulum

The frictional force between a physical damped pendulum and the medium is usually assumed to be 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 experimental observations. For this purpose, 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 non-harmonic 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 no correlation (as is expected) with experimental results.