My-Laplace-Table

My-Laplace-Table - t f 2 3 f sf f s s F s Unit step and...

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Formula for the use of Laplace Transforms to Solve Second Order Differential Equations. Given the differential equation ' y (0) y' ) 0 ( ), ( ' ' ' 0 , 0 y y t g cy by ay we have c bs as t g L ay y b as y L 2 0 0 )) ( ( ' ) ( ) ( We get the solution y(t) by taking the inverse Laplace transform. The following table are useful for applying this technique. Table of Laplace Transforms Definition of Laplace transform 0 ) ( )} ( { dt t f e t f L st )} ( { ) ( 1 s F L t f )} ( { ) ( t f L s F Laplace transforms of elementary functions 1 s 1 n t 1 ! n s n a t 1 ) 1 ( a s a at e a s 1 kt sin 2 2 k s k kt cos 2 2 k s s kt sinh 2 2 k s k kt cosh 2 2 k s s First translation and derivative theorems ) ( t f e at ) ( a s F ) ( t f t n ) ( ) 1 ( s F ds d n n n ) ( ' t f ) 0 ( ) ( f s sF ) ( ' ' t f ) 0 ( ' ) 0 ( ) ( 2 f sf s F s
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Unformatted text preview: ) ( ' ' ' t f ) ( ' ' ) ( ' ) ( ) ( 2 3 f sf f s s F s Unit step and Dirac delta function ) ( a t u s e as ) ( ) ( a t u t f )} ( { a t f L e as ) ( ) ( a t u a t f ) ( s F e as ) ( a t as e Convolution theorem and Laplace transform of a periodic function t d t g f g f ) ( ) ( ) ( ) ( s G s F ) ( ) ( p t f t f p st sp dt e t f e ) ( 1 1...
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My-Laplace-Table - t f 2 3 f sf f s s F s Unit step and...

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