Physics 410/609---Computational Physics
Assignment #3---Due Thursday, October 19
NOTE: At the end of each problem, please indicate how long it took
to solve the problem.
1) Complete Problem 4.5 on page 93 of CSM.
For part (a), you will write a code to solve the motion of a pendulum, as
described in Eq. 4.11. Your code will use the Euler-Richardson
algorithm. One column of output can be the small angle analytic
solution, or you can use awk to compute that as needed in part (b).
For part (c), instead of making multiple graphs of the trajectory
and velocity for different values of initial angle, plot different
cases on a single set of axes.
Note: part a=3points, b=3pts, c=4pts
2) a) Compute the period of the anharmonic oscillator for initial amplitude
1 for various strengths of the potential and determine the relation
between the period and k/m, where the potential is k*x**4/4 .
Use the fourth order Runge-Kutta method for this problem. This
method is explained in Numerical Recipes (see below) and the appendix
of CMS Chapter 5.
To get an accurate value for the period, it is useful to run
several oscillation periods and then divide the time by the number
of periods.
The best way to see the relationship between the period and k/m is
to use a log-log plot.
b) Read sections 16.0-16.4 of Numerical Recipes. If you are looking at
an early edition of the NR, it could be chapter 15. The chapter title
is Integration of Ordinary Differential Equations.