HWsoln9 - EECS 216 1b. s2 +8 s(s2 +16) s2 +8 s(s2 +16)...

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EECS 216 SOLUTIONS TO PROBLEM SET #9 Winter 2008 1. #5.11bcgj: Use the As + B s 2 + a 2 approach for quadratic terms in the denominator. 1b. s 2 +8 s ( s 2 +16) = A s s 2 +16 s 2 +16 + Bs + C s 2 +16 s s = ( A + B ) s 2 + Cs +16 A s ( s 2 +16) A+B=1;C=0;16A=8 A=B= 1 2 . s 2 +8 s ( s 2 +16) = 1 2 1 s + 1 2 s s 2 +16 1 2 u ( t ) + 1 2 cos(4 t ) u ( t ). 1c. 2 s 3 +3 s 2 +6 s +4 ( s 2 +4)( s 2 +2 s +2) = As + B s 2 +4 + Cs + D s 2 +2 s +2 = ( A + C ) s 3 +(2 A + B + D ) s 2 +(2 A +2 B +4 C ) s +(2 B +4 D ) ( s 2 +4)( s 2 +2 s +2) A+C=2; 2A+B+D=3; 2A+2B+4C=6; 2B+4D=4 A=1, B=0, C=1, D=1. 2 s 3 +3 s 2 +6 s +4 ( s 2 +4)( s 2 +2 s +2) = s s 2 +4 + s +1 ( s +1) 2 +1 cos(2 t ) u ( t ) + e - t cos( t ) u ( t ). 1g. 2 s 2 - 6 s +3 s 2 - 3 s +2 = 2 - 1 ( s - 1)( s - 2) = 2 + 1 s - 1 - 1 s - 2 2 δ ( t ) + e t u ( t ) - e 2 t u ( t ). 1j. Delay the answer to (b) above by 2: 1 2 u ( t - 2) + 1 2 cos(4 t - 8) u ( t - 2) 2. #5.12abdf: Compute Laplace transforms, multiply, take inverse Laplace transform. 2a.
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This homework help was uploaded on 04/04/2008 for the course EECS 216 taught by Professor Yagle during the Winter '08 term at University of Michigan.

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