# 3. Laplace transform_upload - Laplace Transform JIN KANG 4...

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Laplace Transform JIN KANG

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4 Step Process Diff Eq. Convert to s domain using Laplace Solve via algebra Convert to time domain 0 ) 0 ( 0 ) 0 ( ) ( 5 ) ( ) ( 6 5 = = = = + x x t u t f t f x x x s s s s X s s X s sX s X s 5 ) 6 5 )( ( 5 ) ( 6 ) ( 5 ) ( 2 2 = + = + ) 1 ( 7 5 ) 6 ( 42 5 6 5 ) ( ) 6 5 ( 5 ) ( 2 + + + = + = s s s s X s s s s X t t e e t x 7 5 42 5 6 5 ) ( 6 + + =
Linearity: can add functions and scale by constant Derivatives 1 st : 2 nd : n th : s s s t u t e ex s BF s AF t f B t f A t Bf t Af t 2 9 3 4 4 5 )] ( 2 3 sin 4 5 [ ) ) ( ) ( )) ( ( )) ( ( )] ( ) ( [ 2 4 2 1 2 1 2 1 + + + + = + + + = + = + L L L L [ ] ) 0 ( ) 0 ( ) 0 ( ) 0 ( ) ( ) ( ) 0 ( ) 0 ( ) ( ) 0 ( ) 0 ( ) ( ) ( 0 ) ( ) 0 ( ) 0 ( ) ( ) ( 1 2 2 1 2 2 2 = = = = = = n n n n n n n f sf f s f s s

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## This note was uploaded on 07/27/2011 for the course MEM 230 taught by Professor Awerbuch during the Spring '08 term at Drexel.

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3. Laplace transform_upload - Laplace Transform JIN KANG 4...

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