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The Elliptic Integrals and the Pendulum Problem

Dr. Ilia Gulkarov

Department of Physics & Astronomy

Northeastern Illinois University

The elliptic integrals of the first and second kinds are applied to describe the small and large oscillations of the simple pendulum. The exact formula for the period of oscillations was derived. This period was expressed in terms of the complete elliptic integral. The circumference of the ellipse was also calculated and expressed in terms of the elliptic integral of the second kind. Numerical calculations of elliptic integrals were performed using the TI-83+ calculator.