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HW4 - ME 391 FALL 2007 HW 4(Due Date Oct 3 2007 1 Use the...

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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 ta- ble) to determine the Laplace transform F(s) for each of the following functions f(t) . (a). t e t t f 6 4 ) ( - + + = (b). < < < = 6 0 6 4 6 4 2 2 2 0 0 ) ( t t t t t f 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) . (a). 3 2 ) 2 ( 4 5 ) ( + + + = s s s s F (b). 45 6 9 2 ) ( 2 + + + = s s s s F 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
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