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MEC-442 – Sistemas de Controle Prof. Fabiano Armellini Tabela de Transformadas de Laplace Função no tempo f(t) Transformada de Laplace F(s) () () = = δ = 0 t , 0 0 t , 1 t t f ( ) 1 s F = () () < = = 0 t , 0 0 t , 1 t u t f () s 1 s F = ( ) t t f = () 2 s 1 s F = ( ) n t t f = () 1 n s ! n s F + = ( ) at e t f - = () a s 1 s F + = ( ) at e t t f - = () ( ) 2 a s 1 s F + = ( ) at n e t t f - = () ( ) 1 n a s ! n s F + + = ( ) ( ) t sen t f ω = () 2 2 s s F ω + ω = ( ) ( ) t cos t f ω = () 2 2 s s s F ω + = ( ) ( ) t sen t t f ω = () ( ) 2 2 2 s s 2 s F ω + ω = ( ) ( ) t cos t t f ω = () ( ) 2 2 2 2 2 s s s F ω + ω - =

Tabela de Transformadas de Laplace - fsa. · PDF fileMEC-442 – Sistemas de Controle Prof. Fabiano Armellini Tabela de Transformadas de Laplace Função no tempo f(t) Transformada

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Page 1: Tabela de Transformadas de Laplace - fsa. · PDF fileMEC-442 – Sistemas de Controle Prof. Fabiano Armellini Tabela de Transformadas de Laplace Função no tempo f(t) Transformada

MEC-442 – Sistemas de Controle Prof. Fabiano Armellini

Tabela de Transformadas de Laplace

Função no tempo f(t)

Transformada de Laplace F(s)

( ) ( )

==δ=

0t,0

0t,1ttf ( ) 1sF =

( ) ( )

<

≥==

0t,0

0t,1tutf ( )

s

1sF =

( ) ttf = ( )2s

1sF =

( ) nttf = ( )

1ns

!nsF

+=

( ) atetf

−= ( )as

1sF

+=

( ) atettf

−⋅= ( )( )2as

1sF

+=

( ) atnettf

−⋅= ( )( ) 1n

as

!nsF

++

=

( ) ( )tsentf ω= ( )22

ssF

ω+

ω=

( ) ( )tcostf ω= ( )22

s

ssF

ω+=

( ) ( )tsenttf ω⋅= ( )( )222s

s2sF

ω+

ω=

( ) ( )tcosttf ω⋅= ( )( )222

22

s

ssF

ω+

ω−=