Final F2009 - Problem #1: _ 2: _ 3: _ 4: _ 5: _ ECE 604...

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ECE 604 LINEAR SYSTEMS Fall 2008 Final Exam Issued: December 10, 2009 Due: 5:00 P. M., December 16, 2009 Instructions The exam is a take-home exam. You should not discuss these problems with others. Do not use Matlab (or any equivalent program such as Mathematica) to generate your answers (you can use any computer program to check your answers). There are six questions with the following values: Problem #1 15 points Problem #2 15 points Problem #3 15 points Problem #4 20 points Problem #5 20 points Problem #6 15 points Total 100 points Consistent with the ECE Honor Code, you are asked to read the following voluntary statement carefully and sign it before beginning your work in each exam booklet: I have not given or received unauthorized aid on this exam. ___________________________________ ___________ Signature Problem #1: _______ 2: _______ 3: _______ 4: _______ 5: _______ 6: _______ Total: _______
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Problem 1: (15 points) Consider the nonlinear vector differential equation: d dt x 1 t ( ) x 2 t ( ) ! " # # $ % & & = x 2 t ( ) x 1 3 t ( ) u t ( ) ! " # # $ % & & (1) a) Assume u t ( ) = sin3 t . Show that x 1 t ( ) = sin t and x 2 t ( ) = cos t is a solution for the initial conditions x 1 0 ( ) = 0 and x 2 0 ( ) = 1 .
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Final F2009 - Problem #1: _ 2: _ 3: _ 4: _ 5: _ ECE 604...

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