Chapter 6.7, Problem 5E

Interpretation Introduction

Interpretation:

To determine the time period $T\left(\alpha \right)$ for the values from $0-180°$ in the steps of $10°$.

Concept Introduction:

The time period of the pendulum, $T\left(\alpha \right)$ governed by the formula $\ddot{\theta }+\sin \theta =0$ can be calculated by expanding the elliptical integral using Binomial series and integrating.

The time period is given by the formula,

$\text{T}\left(\text{α}\right)\text{ = 2π}\left[\text{1 + }\frac{\text{1}}{\text{16}}{\text{α}}^{\text{2}}\text{ + Ο}\left({\text{α}}^{\text{2}}\right)\right]$ for $\text{α < < 1}$

Values of $\alpha$ can be changed by steps of $10°$ from $0-180°$ to find the different values of $T\left(\alpha \right)$.