EEE 244 – Homework Problem 2 -- Due 9/28/05
1. In Homework Problem 1, part 2, consider that there is uncertainty with respect to the
initial value of each of the rail gun parameters: l = 5 mm, m = 1 g, Ro = 100
mBo = 5 mT, Vemf = 5 mV. Find the following:
a. Write an m-file that uses the analytic solution of the problem with constant R and
B, and incorporates the method of section 4.2.2 in your text along with the “root
mean square” error propagation formula given in class, to determine the
uncertainty (u) in the velocity of the bar or wire at time t = 1 s.
b. If we then define the expected percent relative error in velocity as [s = (|u|/u) x
100%] at t = 1 s, how many significant figures should you expect in the
calculation of the predicted bar or wire velocity?
c. Refer to the MATLAB m-file solution to Homework Problem 1, part 2. Modify
the file to determine an “efficient value” of the time increment t (or dt in the
program) for calculation of the bar or wire velocity for the time-dependent R & B
case. Use the expected error determined in part b, and the Centered FDDA
technique for the numerical solution of the differential equation.
d. What assumptions, if any, do you have to make in your calculation of the efficient
time increment here?
e. Plot the bar or wire velocity calculated with this “efficient” time increment over
the range (0 ≤ t ≤ 1 s). Employ the MATLAB “max” command to determine the
maximum velocity and the time of occurrence of the maximum velocity during
the one-second time interval. Use the “gtext” command to display both of the
above on your graph.
2. Draw a flowchart detailed enough to explain to another EEE graduate student how your
MATLAB m-file program, for part 1c above, actually works.
Note: Your submission of this assignment should include a printout of your m-files for parts a, c
and e, and your plot from part e.