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UlsoyPracticeExam1

UlsoyPracticeExam1 - Department of Mechanical Engineering...

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1 Department of Mechanical Engineering The University of Michigan, Ann Arbor ME 360-01, Prof. A. G. Ulsoy (Sec. 1) Modeling, Analysis and Control of Dynamic Systems First Midterm Examination (Closed-book, no calculators, one-page/one-sided of handwritten notes) Winter 2007 February 15, 2007 (8:30 – 10:30 am) Student Name:_____________________ Student ID:___________________ I have neither given nor received any aid on this exam, nor have I concealed any violations of the honor code. Signature:____________________ Note: There are 4 problems. Problem 1 is 30 points, Problem 2 is 20 points, Problem 3 is 20 points and Problem 4 is 30 points. There are 100 points in total. GOOD LUCK!!!

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2 Problem 1. ( Total 30/100 points ) The transfer function of the system is G ( s ) = 4 s 2 + 5 s + 6 = X ( s ) U ( s ) , where U ( s ) denotes Laplace transform of the system input u ( t ) and X ( s ) denotes Laplace transform of the system output x ( t ). (a) What is the differential equation relating the input u ( t ) and output x ( t ) in the time domain? (2/100 points) Answer: __________________________ (b) Input to the system is ) ( 1 3 ) ( t t u ± = , where 1( t ) denotes a unit step input. What is the response for the output of this system in the Laplace domain (i.e. what is
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UlsoyPracticeExam1 - Department of Mechanical Engineering...

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