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ME304_hw1_sol - MIDDLE EAST TECHNICAL UNIVERSITY MECHANICAL...

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ME304/Spring 2005/Sections 02+03+04/HW1Solutions Page 1 / 3 f M 2 M 1 x y 2 y 1 b 2 b 1 k 2 k 1 SOLUTIONS TO HOMEWORK 1 for Sections 02, 03 & 04 Prepared by Gökhan BAYAR (C-204), Atilla BAYRAM (A-148), Erdinç İ Y İ AY (C-209) Problem 1 The differential equations of the model are given by 2 2 2 2 1 1 1 2 1 1 2 1 1 1 ) ( ) ( y k y b x k x b y k k y b b y M + + + = + + + + & & & & & (1) f y k y b y k y b y M + = + + 1 2 1 2 2 2 2 2 2 2 & & & & (2) Taking the Laplace transforms of both sides of these equations gives ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 2 2 2 2 1 1 1 2 1 1 2 1 1 2 1 s Y k s Y s b s X k s X s b s Y k k s Y s b b s Y s M + + + = + + + + (3) ) ( ) ( ) ( ) ( ) ( ) ( 1 2 1 2 2 2 2 2 2 2 2 s F s Y k s sY b s Y k s sY b s Y s M + = + + (4) MIDDLE EAST TECHNICAL UNIVERSITY MECHANICAL ENGINEERING DEPARTMENT ME 304 CONTROL SYSTEMS SPRING 2005
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