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# hw1 - 4 e − t 12 1 2(10 points Determine mathematically...

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EML 4312 Fall 2009 Partial Fraction Expansion The due date for this assignment is Wednesday 9/9. Show your work, and CIRCLE YOUR ANSWER. 1. Determine the inverse Laplace transform for the following problems (i.e., determine f ( t ) ). No partial credit will be given for question #1. a. (10 points) F ( s ) = s + 2 ( s + 1) 3 Is Laplace transform of te t + 1 2 t 2 e t b. (10 points) F ( s ) = ( s + 1) s 2 Is Laplace transform of t + 1 c. (10 points) F ( s ) = 1 ( s + 1)( s + 2)( s + 3) Is Laplace transform of 1 2 e t e 2 t + 1 2 e 3 t d. (10 points) F ( s ) = 5 s ( s + 1)( s + 3) Is Laplace transform of 15 2 e 3 t 5 2 e t e. (10 points) F ( s ) = 5 s 2 + 4 Is Laplace transform of 5 2 sin 2 t f. (10 points) F ( s ) = s 2 ( s 2 + 4) Is Laplace transform of 1 2 cos 2 t g. (10 points) F ( s ) = 2 s ( s 2 + 2 s + 4) Is Laplace transform of 1 2 1 6 3 e 2 t ¡ sin t 3 + 3 cos t 3 ¢ h. (10 points) F ( s ) = 2( s + 3)( s + 2) s ( s + 1) Is Laplace transform of 2 Dirac ( t ) 4 e

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Unformatted text preview: 4 e − t + 12 1 2. (10 points) Determine mathematically and also sketch the step response for part (c) above (i.e., f nd y ( t ) given r ( t ) is a step input) where F ( s ) = Y ( s ) R ( s ) = 1 ( s + 1)( s + 2)( s + 3) . Y ( s ) = 1 s ( s + 1)( s + 2)( s + 3) . , Is Laplace transform of 1 2 e − 2 t − 1 2 e − t − 1 6 e − 3 t + 1 6 5 3.75 2.5 1.25 0.25 0.2 0.15 0.1 0.05 x y 3. (10 points) Apply the IVT and FVT to question 2 to check that your sketch and answer makes sense. IV T → lim t → y ( t ) = lim s →∞ sY ( t ) = s s ( s + 1)( s + 2)( s + 3) = 1 ∞ = 0 FV T → lim t →∞ y ( t ) = lim s → sY ( t ) = s s ( s + 1)( s + 2)( s + 3) = 1 6 2...
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