An analytical solution to the equation of motion for the damped nonlinear pendulum

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  • Kim Johannessen

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An analytical approximation of the solution to the differential equation
describing the oscillations of the damped nonlinear pendulum at large angles
is presented. The solution is expressed in terms of the Jacobi elliptic functions
by including a parameter-dependent elliptic modulus. The analytical solution
is compared with the numerical solution and the agreement is found to be
very good. In particular, it is found that the points of intersection with the
abscissa axis of the analytical and numerical solution curves generally differ
by less than 0.1%. An expression for the period of oscillation of the damped
nonlinear pendulum is presented, and it is shown that the period of oscillation
is dependent on time. It is established that, in general, the period is longer than
that of a linearized model, asymptotically approaching the period of oscillation
of a damped linear pendulum.
JournalEuropean Journal of Physics
Issue number3
Number of pages13
Publication statusPublished - 2014