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 a given arbitrary initial conditions.This solution is expressed in terms of the Multiplexer Jacobian elliptic functions.Approximated trigonometric solution is also provided.Three practical formulas for the period Spill Mop Kits of oscillations are given.The results are illustrated with examples.

Keywords: Undamped pendulum, Duffing equation, Period of oscillations, Jacobian elliptic functions.