Chapter 12.5, Problem 5E

Interpretation Introduction

Interpretation:

To show that there are two stable fixed points in the Poincaré section of the damped driven pendulum, given by $\ddot{\text{θ}}\text{ + b }\dot{\text{θ}}\text{ + sin θ = F cos t}$, with $\text{b = 0}\text{.2, F = 2}$. To describe the corresponding motion of the pendulum in each case. To compute the basins for each fixed point. To show that the boundary between the basins looks like a fractal.

Concept Introduction:

• ➢ The damped driven pendulum is given by $\ddot{\text{θ}}\text{ + b }\dot{\text{θ}}\text{ + sin θ = F cos t}$.

• ➢ The boundary between the basins is called a fractal.