Tabela Laplace

Prévia do material em texto

Tabela de Transformadas de Laplace 
f(t) F(s)= L {f(t)}=



0
st dte f(t)
 
1 1 
s
1
 
2 tn ( n=1,2,...) 
1ns
!n

 
3 tp ( p>-1) 
1ps
)1p(


 
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 
 F(s)G(s) 
19 
)ct( 
 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
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


 
 
Fonte: Stanley Farlow ,“An Introdution to Differential Equations and their Applications”, Mc Graw-Hill