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 ar-13995n give the analytical solution for the undamped pendulum equation for 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 casual azul tequila period of oscillations are given.

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