ECE634S09_HW2solutions

ECE634S09_HW2solutions - ECE634 Signals and Systems II...

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ECE634 Signals and Systems II, Spring 2009 – Homework 2 Solutions Daniel S. Brogan 1 Show all work and write legibly for full credit. 1. Find the inverse Laplace transforms of the following: a) 2 32 41 6 1 8 56 ss sss ++ b) s + c) 2 5 54 s − + + + d) 2 7 71 2 s + + + e) 21 12 6 s s −+ + a) () 22 4 16 18 4 16 18 2 3 2 3 A BC Hs s s s s s s == = + + + + + + 2 0 6 1 8 1 8 3 23 6 s A = = 2 2 6 1 8 1 6 3 2 1 8 2 1 1 2 s B =− + = = +− 2 3 6 1 8 3 6 4 8 1 8 6 2 1 3 s C + = = 31 2 s + ( ) ( ) tt ht e e ut −− ⎡⎤ =− + ⎣⎦ b) 2 3 2 3 A B C s s s s s s = + + + + + + 0 6 1 6 s s A = + = 2 1 0 6 4 2 1 2 s s B + = = 3 1 5 6 9 3 1 3 s s C + = = 12 3 s =+ ( ) ( ) 3 e e c) ( ) 2 55 1 4 1 4 A B s s s s = + + +
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ECE634 Signals and Systems II, Spring 2009 – Homework 2 Solutions Daniel S. Brogan 2 () 1 56 2 43 s s A s =− −+ == = + 4 59 3 13 s s B s = +− 23 14 Hs ss ++ ( ) ( ) 4 tt ht e e ut −− ⎡⎤ ⎣⎦ d) 2 77 7 1 4 A B s s s s = + + + + + 3 74 4 41 s s A s + = + 4 73 3 31 s s B s + = 34 ( ) ( ) e e e) 32 21 12 21 12 63 2 3 2 A B C s s s = + + + − + 0 21 12 12 2 6 s s A = = 3 21 12 63 12 75 5 5 1 5 s s B + = = 2 21 12 42 12 30 3 5 1 0 s s C = + = = + 25 3 s =− + ( ) ( ) 3 e e ut =−+
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ECE634 Signals and Systems II, Spring 2009 – Homework 2 Solutions Daniel S. Brogan 3 2. Find the inverse Laplace transform of () 32 75 25 s Ys sss = + + From homework 1 number 6… 2 15 s ss s =− + ++ ( ) ( ) ( ) 222 2 2 13 2 1 1 1 2 3 12 ss s
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This note was uploaded on 03/05/2009 for the course ECE 651 taught by Professor Messner during the Spring '09 term at New Hampshire.

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ECE634S09_HW2solutions - ECE634 Signals and Systems II...

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