final09sol

final09sol - MAE 143A Signals and Systems Prof. M. Krstic...

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Unformatted text preview: MAE 143A Signals and Systems Prof. M. Krstic FINAL July 31, 2009 NAME: SOLUTIONS Closed book. One sheet (both sides) of handwritten notes allowed. Present your reasoning and calculations clearly. Random or inconsistent etchings will not be graded. Write answers only in the blue book. The problems are not ordered by difficulty. Total points: 50. Time: 2.5 hours. Problem 1. (8 points) Compute the step response of the system H ( s ) = 1 s ( s 2 + 4 s + 8) Solution: Step response is given by L- 1 braceleftBig H ( s ) s bracerightBig . 1 s 2 (( s + 2) 2 + 4) = C 1 s + C 2 s 2 + C 3 s + C 4 ( s + 2) 2 + 4 C 1 = d ds parenleftbigg 1 ( s + 2) 2 + 4 parenrightbiggvextendsingle vextendsingle vextendsingle vextendsingle s =0 =- 2( s + 2) (( s + 2) 2 + 4) 2 vextendsingle vextendsingle vextendsingle vextendsingle s =0 =- 4 64 =- 1 16 C 2 = 1 ( s + 2) 2 + 4 vextendsingle vextendsingle vextendsingle vextendsingle s =0 = 1 8 Matching coefficients, we have 1 =- 1 16 s ( s 2 + 4 s + 8) + 1 8 ( s 2 + 4 s + 8) + ( C 3 s + C 4 ) s 2 0 = parenleftbigg C 3- 1 16 parenrightbigg s 3 + parenleftbigg C 4- 1 4 + 1 8 parenrightbigg s 2 C 3 = 1 16 , C 4 =...
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final09sol - MAE 143A Signals and Systems Prof. M. Krstic...

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