Di¤erential Equations and Matrix Algebra I (MA 221), Fall Quarter, 1999-2000
Quiz 13 – Thursday, November 11, 1999,.due at the end of the class period
BOX
NAMES
00
10 pts 1. Find the steady state solution and the transient solution for x +2x0 +5x = cos(3t); x(0) = 0;
x0 (0) = 0: Give a sketch of the steady state solution, the transient solution, and the solution
on the same set of axes for 0 t 6 (be sure to label the 3 graphs). How long is it before
the transient dies out?
10 pts 2. Fill in the second column of the following table with the amplitude of the steady state
solution for the corresponding frequencies for x00 + 2x0 + 5x = cos(!t); x(0) = 0; x0 (0) = 0:
!
3
4
p2
5
Css
10 pts 3. Use Maple to …nd the solution to x00 + 2x0 + 5x = cos(!t); x(0) = 0; x0 (0) = 0 (you do
not need to write it down). Extract enough information to …nd C(!); the amplitude of the
steady state solution. Give a graph of C(!) vs ! and …nd where C(!) is a maximum.