modeling2

# modeling2 - 4 6 8 3 5 1 Y s s s s X s s s s = Taking the...

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Modeling Q UESTION 2 For the systems described by the differential equations below, determine the transfer functions ( 29 ( 29 Y s X s . a. ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 3 5 4 6 8 y t y t y t y t x t x t x t x t + + + = + + + b. ( 29 ( 29 ( 29 ( 29 ( 29 4 7 5 y t y t y t x t x t + + = + Taking the Laplace transform of ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 3 5 4 6 8 y t y t y t y t x t x t x t x t + + + = + + + with zero initial conditions: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 3 2 3 2 3 5 4 6 8 s Y s s Y s sY s Y s s X s s X s sX s X s + + + = + + + Solving for the transfer function, ( 29 ( 29 3 2 3 2
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Unformatted text preview: 4 6 8 3 5 1 Y s s s s X s s s s + + + = + + + Taking the Laplace transform of ( 29 ( 29 ( 29 ( 29 ( 29 4 7 5 y t y t y t x t x t + + = + &&& & && & with zero initial conditions: ( 29 ( 29 ( 29 ( 29 ( 29 3 2 4 7 5 s Y s sY s Y s s X s sX s + + = + Solving for the transfer function, ( 29 ( 29 2 3 5 4 7 Y s s s X s s s + = + +...
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