4_4a(1) - Solutions 4.4-Page 299 Problem 3 Find the...

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Solutions 4.4-Page 299 Problem 3 Find the convolution . ) ( ) ( t g t f t t g t f sin ) ( ) ( = = Eq.3 states that ( . Direct substitution into Eq.3 yields: τ d t g f t g f t ) ( ) ( ) )( 0 = = 0 )) (sin( sin ) )( ( d t t g f . To evaluate the integral, the trigonometric identity [ cos( ) cos( 2 1 sin sin B A B A = ] ) B A + can be used. Substitution of this identity into the integral yields: [] [] d t t d t t d t t g f t t ) cos( ) 2 cos( 2 1 ) cos( ) cos( 2 1 )) (sin( sin ) )( ( 0 0 0 = + + = = Evaluating the integral yields: [] [ ] () () [] ) sin( cos sin 2 1 2 1 2 1 ) cos( ) 2 cos( 2 1 2 1 2 1 0 0 cos ) 2 sin( t t t t d t t t t t t = = Simplifying yields: 2 cos sin ) )( ( t t t t g f =
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Problem 10 Apply the convolution theorem to find the inverse Laplace transforms of the functions. ) ( 1
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This note was uploaded on 06/06/2011 for the course EGM 3311 taught by Professor Haftka during the Spring '11 term at University of Florida.

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4_4a(1) - Solutions 4.4-Page 299 Problem 3 Find the...

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