Abstract
A highly accurate solution of the nonlinear pendulum with small initial amplitude and damping proportional to the velocity is derived using multi-time scale perturbation methods. The nonlinear pendulum has been studied extensively, but its formulation has rarely incorporated damping. This paper extends the body of traditional results by using a mathematical framework that incorporates damping to get a clear, robust solution in which the interplay of the damping and amplitude yields new physical insights into the pendulum's motion.
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