Chapter 4.4, Problem 3E

Interpretation Introduction

Interpretation:

To sketch $\dot{\text{θ}}\text{ vs t}$ for $\text{θ' = γ - sinθ}$ at different values of $\text{γ}$ including limiting cases $\text{γ}\approx \text{1,}$ $\text{γ >> 1}$.

Concept Introduction:

Overdamped pendulum is an example of a non-uniform oscillator.

The motion of an overdamped pendulum is governed by $\text{θ' = γ - sinθ}$, where $\text{θ}$ is the angle between the pendulum and the downward vertical and $\text{γ}$ is the ratio of applied torque to the maximum gravitational torque.