Dynamics of damped oscillations: physical pendulum
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2017-10-23
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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.
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Quiroga, G. D., & Ospina-Henao, P. A. (2017). Dynamics of damped oscillations: Physical pendulum. Bogotá: doi:10.1088/1361-6404/aa8961