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modeling11

# modeling11 - 29 29 29 29 29 4 4 9 x t x t x t x t f t...

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Modeling Q UESTION 11 For each of the following transfer functions, write the corresponding differential equation. a. ( 29 ( 29 2 4 2 8 5 X s s F s s s = + + b. ( 29 ( 29 ( 29 ( 29 2 9 1 4 X s F s s s = + + c. ( 29 ( 29 3 2 14 3 11 X s s F s s s + = + + Cross multiply ( 29 ( 29 2 4 2 8 5 X s s F s s s = + + to obtain ( 29 ( 29 ( 29 ( 29 2 2 8 5 4 s X s sX s X s sF s + + = and take the inverse Laplace transform with zero initial conditions to obtain ( 29 ( 29 ( 29 ( 29 2 8 5 4 x t x t x t f t + + = & && & Expand ( 29 ( 29 ( 29 ( 29 2 9 1 4 X s F s s s = + + and cross multiply to obtain ( 29 ( 29 ( 29 ( 29 ( 29 3 2 4 4 9 s X s s X s sX s X s F s + + + = . Take the inverse Laplace transform with zero initial conditions to obtain
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Unformatted text preview: ( 29 ( 29 ( 29 ( 29 ( 29 4 4 9 x t x t x t x t f t + + + = &&& && & Cross multiply ( 29 ( 29 3 2 14 3 11 X s s F s s s + = + + to obtain ( 29 ( 29 ( 29 ( 29 ( 29 3 2 3 11 14 s X s s X s X s sF s F s + + = + and take the inverse Laplace transform with zero initial conditions to obtain ( 29 ( 29 ( 29 ( 29 ( 29 3 11 14 x t x t x t f t f t + + = + & &&& &&...
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