Finding the Period of a Simple Pendulum using the Taylor Series Expansion vs the Simple Pendulum

by Nicholas Miller

Submitted : Fall 2019

This project revolves around the use of two formulas, the simple pendulum formula and the Taylor Series expansion. The simple pendulum formula requires simple rearranging of basic physic formulas and algebraic substitution which led to the simple pendulum period equation. The equation states that only the length of the pendulum arm and the force of gravity affect the period of oscillation. The Taylor Series Expansion proves the small angle theorem for SIN to be useful, stating that the SIN of all angles less than 15 can be used without the use of the SIN function. From there, you can simply use the formula to where you can find the period of oscillation by only using the length and the force of gravity. If needed, the force of gravity can be found by rearranging the formula to where the time it takes for the pendulum to oscillate is divided by the length of the pendulum arm. 

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