hw8soln

# hw8soln - Question 1: a) F ( s ) = 1 2 + s s +1 f (t ) = u...

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Question 1: a) b) c) d) ) ( 11 ) ( 3 ) ( 4 11 3 1 3 ) 4 ( 4 1 3 ) ( 4 t u e t t g s s s s s s G t = + = + + = + + = δ ) ( ) ( 2 ) ( 3 2 1 2 ) ( ) 3 ( ) 1 ( ) 3 )( 1 ( 4 ) ( 3 t u e e t h s s s H s B s A s s s H t t = + + + = + + + = + + = ) ( 2 ) ( ) ( 1 2 1 ) ( t u e t u t f s s s F t + = + + = 2 ) ( ) 3 ( 2 ) ( ) 1 ( 3 1 = + = = + = = = s s s H s B s H s A ) 4 ( ) 2 ( ) 2 ( ) 4 ( ) 2 ( 12 ) ( 2 2 + + + + + = + + = s C s B s A s s s J Now set s equal to zero in J(s) to find B: Question 2: Note that roots of are complex 3 2 9 3 4 3 2 4 6 16 12 ) ( 0 = + = + + = = = B B B s J s ) ( ) 3 3 6 ( ) ( ) 4 ( 3 ) 2 ( 3 ) 2 ( 6 ) ( 4 2 2 2 t u e e te t j s s s s J t t t + = + + + + + = 3 ) ( ) 4 ( 6 ) ( ) 2 ( 4 2 2 = + = = + = = = s s s J s C s J s A ) 13 4 ( ) 13 4 ( 26 2 ) ( 2 2 + + + + = + + + = s s C Bs s A s s s s s V ) 13 4 ( 2 + + s s

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Now multiply out factors to find B: 6 2 ) ( ) 13 4 ( 2 s s s C Bs s s A + = + + + + s Cs As Bs As 2 4 0 2 2 = + = + Question 3: b) Question 4: b) () ) ( ) cos( ) ( ) cos( ) ( 1 1 ) ( 2 2 π = = + = + = t u t t u t t f s s e s se s F st s 2 ) ( ) ( 0 = = = s s V s A 6 4 2 2 = = = = A C A B ) ( ) 3 sin( 3 2 ) 3 cos( 2 2 ) ( 3 ) 2 ( 3 3 2 3 ) 2 ( 2 2 2 3 ) 2 ( 1 2 3 ) 2 ( 2 2 2 3 ) 2 ( 3 2 2 13 4 ) 2 ( 3 2 2 ) 13 4 ( 6 2 2 ) ( 2 2 2 2 2 2 2 2 2 2 2 2 2 2 t u t e t e t v s s s s s s s s s s s s s s s s s s s V t t
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## This note was uploaded on 01/19/2012 for the course EECE 253 taught by Professor Shuo,tang during the Spring '11 term at UBC.

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hw8soln - Question 1: a) F ( s ) = 1 2 + s s +1 f (t ) = u...

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