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Tabela de Transformadas de Laplace f(t) F(s)= L {f(t)}= 0 st dte f(t) 1 1 s 1 2 t n ( n=1,2,...) 1ns !n 3 t p ( p>-1) 1ps )1p( 4 e at as 1 5 e at t n ( n=1,2,...) 1n)as( !n 6 sin bt 22 bs b 7 cos bt 22 bs s 8 sinh bt 22 bs b 9 cosh bt 22 bs s 10 e at sin bt 22 b)as( b 11 e at cos bt 22 b)as( as 12 u (t - c) s e cs 13 u(t - c)f( t- c) )s(Fe cs 14 t sin at 222 )as( as2 15 t cos at 222 22 )as( as 16 sin at – at cos at 222 3 )as( a2 17 sin at + at cos at 222 2 )as( as2 18 t 0 d)(g)t(f F(s)G(s) 19 )ct( e -cs 20 )t(f )n( )0(f...)0(fs)s(Fs )1n(1nn 21 t n f(t) )s(F)1( )n(n 22 f(t+T)=f(t) sT T 0 st e1 dte Fonte: Stanley Farlow ,“An Introdution to Differential Equations and their Applications”, Mc Graw-Hill PROPRIEDADES Transformada de Laplace Transformada Inversa de Laplace L {f +g}=L {f} + L {g} L -1 {F +G}=L -1{F} + L -1{G} L {cf } = cL {f} L --1 {cF }= cL -1{F} L {f ’}= sL {f}- f(0) L –1{F(s)}= n n 1 n n ds )s(Fd t )1( L L {f ’’}= s2L {f}- sf(0) – f ’(0) L –1 s )s(F = d)(f t 0 L {f (n)}= snL {f} - sn-1f(0) - sn-2f’(0) - ... - f(n-1)(0) L -1 (F(s - a)) = eatf(t) L {eatf(t)}=F(s - a) L )s(F ds d )1()t(ft n n nn L a s F a 1 )at(f L gf L {f}L {g} L )s(F s 1 d )(f t 0 L s d )(F t )t(f )0(f)s(sFlim s )(f)s(sFlim 0s
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