Chapter 4.4, Problem 1E

Interpretation Introduction

Interpretation:

To find the conditions under which it is valid to approximate the equation ${\text{mL}}^{\text{2}}\ddot{\text{θ}}\text{ + b}\dot{\text{θ}}\text{ + mgL sin θ = Γ}$ by its overdamped limit $\text{b}\dot{\text{θ}}\text{ + mgL sin θ = Γ}$.

Concept Introduction:

If $\text{Γ}$ is the constant torque applied on a pendulum, then its general equation is given by

${\text{mL}}^{\text{2}}\ddot{\text{θ}}\text{ + b}\dot{\text{θ}}\text{ + mgL sin θ = Γ}$, where

$\text{m}$ is the mass of the pendulum, $\text{L}$ is the length of the pendulum, $\text{b}$ is a viscous damping constant, and $\text{g}$ is the acceleration due to gravity.