# 4_4b - Solutions 4.4-Page 299 Problem 16 Apply either...

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Solutions 4.4-Page 299 Problem 16 Apply either Theorem 2 or Theorem 3 to find the Laplace transform of . ) ( t f t t t f 2 cos ) ( 2 = Eq.8 (Theorem 2) states that { } ) ( ) 1 ( ) ( ) ( s F t f t n n n = L . Substituting the given into Eq.8 yields: ) ( t f {} + = 2 2 2 2 2 2 ) 1 ( 2 cos s s s d d t t L , where { } t 2 cos L is determined from Figure 4.1.2 on pg.268. Differentiating twice yields: {} 3 2 3 2 ) 4 ( 24 2 2 cos + = s s s t t L

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Apply either Theorem 2 or Theorem 3 to find the Laplace transform of . ) ( t f t e t f t 1 ) ( 3 = Eq.12 of Theorem 3 states that = s d F t f(t) σ ) ( L where is a variable of integration. Using Theorem 3, {} [ ] () ( [] ) ln( ) 3 ln( ) ln( ) ln( 1 3 1 1 1 ) 3 ln( 3 3 s s d d - e t e s s s t t = = = = σ L L ) ln ln 1 3 s s t e t
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4_4b - Solutions 4.4-Page 299 Problem 16 Apply either...

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