modeling9

# modeling9 - =-=-= = âˆ âˆ âˆ For f t = sin Ï‰t 29 29 29 29...

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Modeling Q UESTION 9 Derive the Laplace transforms for the following time functions: a. f ( t ) = 1 b. f ( t ) = t c. f ( t ) = 1– e at d. f ( t ) = sin( ωt ) For f ( t ) = 1, ( 29 ( 29 0 0 0 1 1 st st st F s f t e dt e dt e s s - - - - - - = = = - = For f ( t ) = t , ( 29 ( 29 ( 29 2 2 0 0 0 1 1 st st st e st F s f t e dt te dt s s - - - - - - + = = = - = For f ( t ) = 1– e at : ( 29 ( 29 ( 29 ( 29 ( 29 0 0 0 0 1 1 1 1 1 s a t s a t st at st st st F s f t e dt e e dt e e dt e e s s a s s a - - - - - + - + - - - - - =
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Unformatted text preview: =-=-= -+ =- + + âˆ« âˆ« âˆ« For f ( t ) = sin( Ï‰t ): ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 sin sin cos st st st e F s f t e dt t e dt s t t s s Ï–---âˆž âˆž âˆž---= = = ---= + + âˆ« âˆ«...
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