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modeling1 - = =-= For f t = cos ωt 29 29 29 29 29...

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Modeling Q UESTION 1 Derive the Laplace transforms for the following time functions: a. f ( t ) = 1 b. f ( t ) = t c. f ( t ) = e at d. f ( t ) = cos( 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 ) = e at , ( 29 ( 29 ( 29 ( 29 0 0 0 0 1 1 s a t s a t st at st F s f t e dt e e dt e dt e s a s a - - - - + - + - - -
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Unformatted text preview: = = -= + + ∫ ∫ ∫ For f ( t ) = cos( ωt ): ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 cos cos sin st st st e s F s f t e dt t e dt s t t s s ϖ---∞ ∞ ∞---= = = --+ = + + ∫ ∫...
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