HW4 - ME 391 FALL 2007 HW 4(Due Date Oct 3 2007 1 Use the definition of the Laplace transform(that is do the integration directly do NOT use a

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Unformatted text preview: ME 391: FALL 2007 HW 4 (Due Date: Oct. 3, 2007) 1. Use the definition of the Laplace transform (that is, do the integration directly, do NOT use a table) to determine the Laplace transform F(s) for each of the following functions f(t). (a). f (t ) = 4 + t + e -6t 0 0 t < 2 2 2 t < 4 (b). f (t ) = 6 4 t < 6 0 t6 2. Use partial fraction expansions and a table of known Laplace transforms to determine the inverse transform f(t) for the following functions F(s). s 2 + 5s + 4 F (s) = (a). ( s + 2) 3 2 + 9s (b). F ( s ) = 2 s + 6 s + 45 3. Solve the following initial value problems by taking Laplace transform of the equation, solving for Y(s), breaking it up into partial fractions and taking inverse Laplace transform to find y(t). (a). y + y = e -7 t , y (0) = 4 (b). y - 9 y = e -3t , y (0) = 0, y (0) = 0 4. Use the s-translation property (first translation theorem) and a table of known Laplace transforms to solve these problems. (a). Determine F(s) = L {e 2t cos 2 3t} 16( s + 4) 2 (b). Determine f(t) = L 2 2 [( s + 4) + 16] -1 5. Practice Problems (do not submit for grading) Exercises 4.1: Problems 6, 10, 17, 30, 35, 36, 39, 40, 46 Exercises 4.2: Problems 2, 8, 22, 26, 34, 36, 39, 41, 42 Exercises 4.3: Problems 4, 5, 15, 20, 22, 25, 26, 29 ...
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This note was uploaded on 07/25/2008 for the course ME 391 taught by Professor Blazer-adams during the Fall '08 term at Michigan State University.

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