PH3110

HW6 Problem #2. COMP2 (10 pts)

• For the following exercise you may use the Runge-Kutta tool kit (rungekutta.html) I have prepared in Fortran in a Unix environment. You may use Matlab instead, if you wish, but I will not be able to help you if you get stuck using Matlab.

• Modify the derive.for file to change the drag term to be proportional to speed squared (see problem C3.2 in the textbook).

• Using the initial conditions x(0)=1.0d0 and v(0)=0.0d0, vary gamma and see if you can find a well-defined value for critical damping. Do you think there is a "critical damping" like in the linear case? If not, is there something analogous? Plot x(t) for gamma = 0 as well as several non-zero values to show the general trends as gamma changes. Comment on your results, including how the period changes, how the amplitude changes, and how slow or how fast the mass comes to equilibrium in the different cases.