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4_3a - = a in the translation theorem Therefore t e t t f 2...

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Solutions 4.3-Page 291 Problem 1 Apply the translation theorem to find the Laplace transforms of the functions. t e t t f π 4 ) ( = The translation theorem states that . ) ( )} ( { a s F t f e at = L For this problem, and 4 ) ( t t f = = a . Therefore 5 5 4 ) ( 24 ) ( ! 4 } { = = s s t e t L

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Problem 3 Apply the translation theorem to find the Laplace transforms of the functions. t e t f t π 3 sin ) ( 2 = The translation theorem states that . ) ( )} ( { a s F t f e at = L For this problem, t t f 3 sin ) ( = and 2 = a . Therefore 2 2 2 9 ) 2 ( 3 } 3 sin { + + = s t e t L
Problem 7 Apply the translation theorem to find the inverse Laplace transforms of the functions. 4 4 1 ) ( 2 + + = s s s F ) ( s F can be rewritten as 2 ) 2 ( 1 ) ( + = s s F . This transform corresponds to an inverse of the form . However we have t t f = ) ( 2 + s instead of . So s 2

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Unformatted text preview: = a in the translation theorem. Therefore t e t t f 2 ) ( − = Problem 9 Apply the translation theorem to find the inverse Laplace transforms of the functions. 25 6 5 3 ) ( 2 + − + = s s s s F ) ( s F can be rewritten as 16 ) 3 ( 14 16 ) 3 ( ) 3 ( 3 16 ) 3 ( 9 5 ) 3 ( 3 ) ( 2 2 2 + − + + − − = + − + + − = s s s s s s F t t t f sin cos ) ( . This transform corresponds to an inverse of the form + = . However we have instead of s . So in the translation theorem. 3 − s 3 = a Therefore ) 4 sin ) 2 / 7 ( 4 cos 3 ( ) ( 3 t t e t f t + =...
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4_3a - = a in the translation theorem Therefore t e t t f 2...

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