5. (5 pt) Now consider the damped and undriven case, $\gamma$ = 0. What is the equation of motion in this case?
Can you develop this equation of motion fully from a potential (like we did above)? If so, what is the
potential? If not, why not?
6. (5 pt) Plot the phase space for the damped and undriven case. What kinds of trajectories are there?
7. (10 pt) Here you are likely to need a numerical solver. Solve the equation of motion for the damped and
undriven case for a reasonable choice of $\alpha$, $\beta$, $\delta$, and initial conditions. Plot the position as a function of
time. What is the behavior of the system? Does it match your expectations from the phase portrait?
Driven and damped case (20 points)
8. (5 pt) Now consider the damped and driven case, $\gamma \neq$ 0. What is the equation of motion in this case? Can
you develop this equation of motion fully from a potential (like we did above)? If so, what is the potential?
If not, why not?
9. (5 pt) Is it possible to plot the phase space for the driven and damped case? Why or why not? What
solutions are available to you to understand the behavior of the system in phase space? Here we are not
looking for you to solve the problem, but to conduct research into how people make sense of the behavior of
driven and damped systems.
10. (10 pt) Here you are likely to need a numerical solver. Solve the equation of motion for the driven and
damped case for a reasonable choice of $\alpha$, $\beta$, $\delta$, $\gamma$, $\omega$, and initial conditions. Plot the position as a function
of time. What is the behavior of the system?
