Dynamics of damped oscillations: physical pendulum

QUIROGA, G D; OSPINA-HENAO, P A

EUROPEAN JOURNAL OF PHYSICS

IOP PUBLISHING LTD

Año: 2017 vol. 38

0143-0807

The frictional force between a physical damped pendulum and the medium isusually assumed to be proportional to the pendulum velocity. In this work, weinvestigate how the pendulum motion will be affected when the drag force ismodeled using power-laws bigger than the usual 1 or 2, and we will show thatsuch assumption leads to contradictions with experimental observations. Forthis purpose, a more general model of a damped pendulum is introduced,assuming a power-law with integer exponents in the damping term of theequation of motion, and also in the non-harmonic regime. A Runge?Kuttasolver is implemented to compute the numerical solutions for the first fivepowers, showing that the linear drag has the fastest decay to rest, and thatbigger exponents have long-time fluctuation around the equilibrium position,which have no correlation (as is expected) with experimental results.