Midterm1 - Name_SOLUTION(Please Print Georgia Institute of...

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Name:___SOLUTION _______________________(Please Print) Georgia Institute of Technology Woodruff School of Mechanical Engineering ME3015 System Dynamics and Control First mid-term: February 26, 2002 You need to show all the work clearly. Only answers or partial steps are not acceptable. Transfer functions must be written in standard form: G(s) =N(s)/D(s) where N(s) and D(s) are polynomials of “s” in descending order. All problems are equally weighed. Answer three of the four problems. Closed book/ closed notes, one-page formula sheet (with no examples) must be turned in with the test. Check problem to be graded: Problem 1:_____ Problem 2:_____ Problem 3:_____ Problem 4:_____.
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[1] (33.33%) Consider the following mechanical system, where ) ( 1 t x and ) ( 2 t x are the displacements of the masses and ) ( t f is an force external input. (a) Derive the equations of motion for ) ( 1 t x and ) ( 2 t x . (Common mistakes: sign error in the k 2 term) See solution to text problem ) ( 2 1 1 1 1 1 1 1 1 x x k x k x b f x m = ± ± ± ) ( 2 1 2 1 2 2 2 x x k x b x m + = ± ± ± 2 2 1 2 1 1 1 1 1 ) ( x k f x k k x b x m + = + + + ± ± ± (1) 1 2 2 2 2 2 2 2 x k x k x b x m = + + ± ± ± (2) (b) Obtain the transfer function ) ( ) ( 2 s F s X . Note there are two unknowns, ) ( 1 t x and ) ( 2 t x . Since we are interested in ) ( 2 t x , we eliminate ) ( 1 t x by substituting it from Equation (2) into Equation (1).
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Midterm1 - Name_SOLUTION(Please Print Georgia Institute of...

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