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Tabela de Transformadas de Laplace
f(t) F(s)= L {f(t)}= ∫+∞
−
0
stdte f(t)
1 1 s
1
2 tn ( n=1,2,...) 1ns
!n+
3 tp ( p>-1) 1ps
)1p(+
+Γ
4 eat
as
1
−
5 eattn ( 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 eatsin bt 22 b)as(
b
+−
11 eatcos 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 τττ F(s)G(s)
19 )ct( −δ e-cs
20 )t(f )n( )0(f...)0(fs)s(Fs )1n(1nn −− −−−
21 tnf(t) )s(F)1( )n(n−
22 f(t+T)=f(t)
sT
T
0
st
e1
dte
−
−
−
∫
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
n1
n
n
ds
)s(Fd
t
)1(L
L {f ’’}= s2L {f}- sf(0) – f ’(0) L –1
s
)s(F= ττ 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(Fds
d)1()t(ft
n
nnn −=
L { }
=
a
sF
a
1)at(f
L { }=∗ gf L {f}L {g}
L )s(Fs
1d )(f
t
0
=
∫ ττ
L ∫∞
=
s
d )(Ft
)t(fεε
)0(f)s(sFlims
=∞→
)(f)s(sFlim0s
∞=→
Fonte: Stanley Farlow ,“An Introdution to Differential Equations and their Applications”, Mc Graw-Hill
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