Analytic solution to the pendulum equation for a given initial conditions

Analytic solution to the pendulum equation for a given initial conditions

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In this paper we give the analytical solution for the undamped pendulum equation for giantmouse jagt a given arbitrary initial conditions.This solution is expressed in terms of the Jacobian elliptic functions.Approximated trigonometric solution is also provided.Three practical formulas for the adifom q red period of oscillations are given.

The results are illustrated with examples.Keywords: Undamped pendulum, Duffing equation, Period of oscillations, Jacobian elliptic functions.