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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.