pset4_sol

# pset4_sol - ME3015 PROBLEM SET#4(25 points SOLUTIONS 1(8...

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ME3015 PROBLEM SET #4 (25 points). SOLUTIONS 1. (8 points) Derive the transfer function of the electrical system ) ( / ) ( s E s E i O shown below. Draw a schematic diagram of an analogous mechanical system. Solution (1) Define impedances s C R Z 1 1 1 1 s C R Z 2 2 2 1 . Hence, 1 2 2 2 2 1 2 2 2 2 1 1 2 2 2 1 2 1 ) ( 1 1 1 1 ) ( ) ( C C s C R C R C R s C R s C R s C R Z Z Z s E s E i O .(ANS) If we change 2 2 1 1 2 2 1 1 / 1 , / 1 , , k C k C b R b R , then we have 2 1 2 2 1 2 2 1 2 2 2 2 1 2 2 1 1 ) ( 1 1 1 ) ( 1 k k s k b b s k b C C s C R C R C R . Consider a mechanical system whose transfer function is given by 2 1 2 1 2 2 ) ( ) ( ) ( k k s b b k s b s X s X i O . This analogous mechanical system is shown as follows. (ANS) e i ( t ) e o ( t ) R 1 R 2 C 1 C 2 k 1 x i b 1 x O k 2 b 2

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Solution (2) You can work on the equations: I s C R s E I s C R s C
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pset4_sol - ME3015 PROBLEM SET#4(25 points SOLUTIONS 1(8...

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