# 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 $$\phi$$?

$$\phi$$: