### AME 301: Differential Equations, Vibrations and Control Homework 12

 B. GoodwineJ. Lucey Fall, 2003 Issued: December 5, 2003 Due: December 10, 2003 (US)11 December 2003 (UK)

1. Consider

1. Determine the exact solution (10 points).
2. Using Euler's method, write a computer program in any language other than a matlab to determine an approximate solution to the equation (20 points).
3. Using the fourth order Runge-Kutta method, write a computer program in any language other than matlab to determine an approximate solution to the equation (20 points).
4. In addition to submitting your work for the exact solution and a listing of each program, submit the a figure plotting the exact solution, the solution from Euler's method and the solution from the fourth order Runge-Kutta method on the same plot from to (5 points each):

2. Consider

1. Using Euler's method, write a computer program in any language other than a matlab to determine an approximate solution to the equation (5 points).
2. Using the fourth order Runge-Kutta method, write a computer program in any language other than matlab to determine an approximate solution to the equation (5 points).
3. In addition to submitting a listing of each program, submit a figure plotting the solution from Euler's method and the solution from the fourth order Runge-Kutta method on the same plot from t=0 to t=10 for (5 points each):
4. For the same time steps (except for part (c)(i)), submit three plots where the time range is from to (10 points total).
5. Explain what happens between and (20 points).

Last updated: December 5, 2003.
B. Goodwine (goodwine@controls.ame.nd.edu)
J. Lucey (jlucey@nd.edu)