HWK3514_HWK_6_solution_Fall_2007

HWK3514_HWK_6_solution_Fall_2007 - ME 3514 System Dynamics...

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ME3514 - HWK - Burdisso - 54 ME 3514 – System Dynamics HOMEWORK #6-Solution DUE: DUE: 10/26/07 1. (10pts) Solve problem B-6-8 (Book page 314) Solution: Assume 12 ii > For above figure, () ( ) 1 1 0.................. 1 i di et L i i d t dt C −− −= ( ) 22 1 2 1 0......... 2 Ri i i C + = Taking the Laplace Transform () () [] 1 ........ .......... 1 2 1 1 s E s I s I Cs s LsI i = + 2 ......... 0 1 1 2 2 2 2 1 = + + s I s I Cs s I R s I R In Matrix Form = + + + 0 1 1 1 1 2 1 2 1 s E s I s I Cs R R Cs Cs Cs Ls i Or + + + = 0 1 1 1 1 1 2 1 2 1 s E Cs R R Cs Cs Cs Ls s I s I i Or NAME:
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ME3514 - HWK - Burdisso - 55 () + + + + + + = 0 1 1 1 1 1 1 1 1 2 1 2 2 2 1 2 1 s E Cs Ls Cs Cs Cs R R s C Cs R R Cs Ls s I s I i Taking s I 2 from Matrix form ( ) 3 . .......... 1 1 1 1 2 2 2 1 2 + + + = s C Cs R R Cs Ls Cs s E s I i Also From figure we have, ( ) 4 . .......... .......... .......... 2 2 R s E s I o = Equating (3) and (4) ( ) + + + = 2 2 2 1 2 1 1 1 1 s C Cs R R Cs Ls Cs s E R s E i o + + + + + = 2 2 2 2 2 1 2 1 2 1 1 1 1 s C s C R R Cs C L R R Ls Cs R s E s E i o Simplifying 2 1 2 2 1 2 R R Ls Cs R R L R s E s E i o + + + + =
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ME3514 - HWK - Burdisso - 56 2. (10 pts) Solve problem B-6-10 (Book page 315) Solution: Using the approach as before leads to () ( ) ( ) [ ] ( ) ( ) 1 ........ ..........
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HWK3514_HWK_6_solution_Fall_2007 - ME 3514 System Dynamics...

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