04spfin - d x 1 d t = x 1 + 2 x 2 + e-t d x 2 d t = 3 x 2 +...

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Math 320 Final Exam May 11, 2004, 7:45 am, B239 Van Vleck M´arton Bal´azs NAME: 1. (60 points) Solve d x 1 d t = - 3 x 1 + 2 x 2 d x 2 d t = - x 1 - x 2 , x 1 (0) = 1 x 2 (0) = 1 .
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2. (50 points) Determine the natural modes and the corresponding frequencies of the following mass-spring system: / / / / / \\\\\\\\\\ ////////// 2 / / / / / / / / / / / / / / / / / / / / / / / \\\\\\\\\\ ////////// 1 4 2 (Numbers above the springs represent the spring constants, and numbers in the bodies stand for the masses.)
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3. (60 points) Use fundamental matrices and variation of parameters to solve
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Unformatted text preview: d x 1 d t = x 1 + 2 x 2 + e-t d x 2 d t = 3 x 2 + e t , x 1 (0) = 2 x 2 (0) = 1 . 4. (30 points) Use Gauss-Jordan elimination to solve the system 3 x 1 + x 2 = 5 x 1 + x 2 + 2 x 3 = 9 4 x 1-2 x 2-x 3 =-3 . 5. (40 points) Solve the initial value problem of the damped and forced resonance d 2 x d t 2 + 2 d x d t + 2 x = cos t, x (0) = 0 , x p (0) = 0 . Also Fnd the amplitude of the asymptotic motion (valid after a long time)....
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This note was uploaded on 08/11/2008 for the course MATH 475 taught by Professor Balazs during the Fall '05 term at Wisconsin.

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04spfin - d x 1 d t = x 1 + 2 x 2 + e-t d x 2 d t = 3 x 2 +...

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