Chapter 11, Exploration 30

The tool here plots the dynamics of equation 11.7 from the text. The inital condition is labelled \(A\), and may be dragged around the board. For each of the following values of \(phi\), answer the questions below. \[ \phi = \pi/4, \hspace{.05in} \phi = \pi/2, \hspace{.05in} \phi = \pi, \hspace{.05in} \phi = \pi/10, \hspace{.05in} \phi = \pi / \sqrt 2 \]

• Do the dynamics that you see depend on the initial condition?
• Is the fixed point (0,0) a sink, a source, a saddle, or none of these?
• Are the dynamics periodic or not? If they are what is the period and how does this relate to \(\phi\)?