Review Problem 1 solution

# Review Problem 1 solution - 2 0 s F s sf f-d The Laplace...

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1. Find the Laplace Transform of ( ) 2 2 2 5 d x dx x u t dt dt + + = subject to an arbitrary input and arbitrary initial conditions ( ) 0 x and ( ) 0 x d . Solve for ( ) X s in terms of the arbitrary input and initial conditions. From Laplace Transform Table: The transform of ( ) n n d f t dt is ( ) ( ) ( ) 1 1 2 1 0 0 0 n n n n n t d f s F s s f s f dt - - - - = - - - - d . If 1 n = , the transform is ( ) d f t dt and ( ) ( ) 0 sF s f - while for 2 n = the pair is ( ) 2 2 d f t dt and ( ) ( ) ( )
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Unformatted text preview: 2 0 . s F s sf f--d The Laplace Transform of the differential equation is thus, ( ) ( ) ( ) ( ) 2 2 5 s X s sx x sX s x X s U s --+-+ = d ( ) ( ) ( ) 2 2 5 2 s s X s U s s x x + + = + + + d ( ) ( ) ( ) 2 2 2 2 5 2 5 U s s x x X s s s s s + + = + + + + + d...
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## This note was uploaded on 02/29/2008 for the course ME 242 taught by Professor Perreira during the Spring '08 term at Lehigh University .

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