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+ 3cos t 3 ¢ h. (10 points) F ( s )= 2( s +3)( s +2) s ( s +1) Is Laplace transform of 2Dirac( t )
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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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This note was uploaded on 09/05/2011 for the course EML 4312 taught by Professor Dixon during the Fall '07 term at University of Florida.

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hw1 - 4 e t + 12 1 2. (10 points) Determine mathematically...

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