hw7_sol - MEEN 364 Fall 2004 Homework Set 7 Due October 21,...

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MEEN 364 Homework Set 7 Fall 2004 October 15, 2004 Homework Set 7 – Due October 21, 2004 @ 5:00 PM 1. Two degree of freedom system: The free body diagram The governing differential equations are: 11 2 1 22 1 2 mx F Kx m x Kx Kx =+ =− && ( 1 ) Taking the Laplace transforms of the first equation, we get 2 2 2 1 2 m s X F KX KX msX KX 1 ( 2 ) From equation (2), we get 2 1 () ms K X X K + = Substituting the value of X1 from the above equation to equation (1), we get 2 12 1 2 X K F smm s K m K m = ++ ( 3 ) Equation (3) denotes the transfer function of the system. 2. (a) We have the system u x x 4 3 + = & x y 2 = Taking Laplace transform and assuming the initial condition is x ( t 0 ) =0, we get ) ( 2 ) ( ) ( 4 ) ( 3 ) ( s X s Y s U s X s sX = + = Simplifying the first of these equations, 1
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MEEN 364 Homework Set 7 Fall 2004 October 15, 2004 ) ( 4 ) ( ) 3 ( ) ( 3 ) ( s U s X s s X s sX = + = + ) ( ) 3 ( 4 ) ( s U s s X + = Substituting this result in the output equation, we get ) ( 3 4 2 ) ( s U s s Y + = Thus the transfer function of the given system is 3 8 ) ( ) ( ) ( + = = s s U s Y s P (b)
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This note was uploaded on 04/18/2010 for the course MEEN 364 taught by Professor Staff during the Spring '08 term at Texas A&M.

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hw7_sol - MEEN 364 Fall 2004 Homework Set 7 Due October 21,...

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