# 4_1b - Solutions 4.1-Page 273 Problem 25 Use the transforms...

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Solutions 4.1-Page 273 Problem 25 Use the transforms in Fig. 4.1.2 to find the inverse Laplace transforms of the functions. 2 / 5 2 1 ) ( s s s F = From Fig. 4.1.2, s 1 corresponds to 1 ) ( = t f . The form of 2 / 5 2 s corresponds to with a t t f = ) ( 2 / 3 = a . π ) 4 / 3 ( ) 2 / 1 ( ) 2 / 1 )( 2 / 3 ( ) 1 2 / 1 ( ) 2 / 3 ( ) 2 / 3 ( ) 2 / 3 ( ) 1 2 / 3 ( = Γ = + Γ = Γ = + Γ because = Γ ) 2 / 1 ( according to pg.267. The form of the inverse Laplace function must be multiplied by 3 8 to get the correct function. 3 8 1 ) ( 2 / 3 t t f =

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Use the transforms in Fig. 4.1.2 to find the inverse Laplace transforms of the functions. 9 3 5 ) ( 2 + = s s s F The transform can be rewritten as 9 3 9 5 ) ( 2 2 + + = s s s s F 9 5 2 + s corresponds to an inverse of the form sin where kt 3 = k . With , the inverse is 3 = k 9 3 2 + s . This inverse must be multiplied by 5/3 in order to get 9 5 2 + s . 9
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4_1b - Solutions 4.1-Page 273 Problem 25 Use the transforms...

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