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. $$\varphi =\pi /4,\varphi =\pi /2,\varphi =\pi ,\varphi =\pi /10,\varphi =\pi /\sqrt{2}$$

• 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 $\varphi$?