Tabela_Transformadas de Laplace

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Tabela de Transformadas de Laplace
Func¸a˜o Transformada de Laplace Domı´nio
1. k, constante
k
s
s > 0
2. tn, n = 1, 2, 3, ...
n!
sn+1
s > 0
3. t−1/2
√
pi
s
s > 0
4. ek t
1
s− k s > k
5. sin (k t)
k
s2 + k2
s > 0
6. cos (k t)
s
s2 + k2
s > 0
7. sinh (k t)
k
s2 − k2 s > | k |
8. cosh (k t)
s
s2 − k2 s > | k |
9. ek t f(t) F (s− k) = L{f(t)}s→ s−k s− k ∈ DF
10. f(t− a)U(t− a) e−a s F (s) s ∈ DF
11. f(t)U(t− a) e−a s L{f(t+ a)}
12. tn f(t), n = 1, 2, ... (−1)n d
nF (s)
d sn
13. f (n)(t), n = 1, 2, ... sn F (s)− sn−1 f(0)− sn−2 f ′(0)− ...− f (n−1)(0) s ∈ DF
14.
∫ t
0
f(y) g(t− y) dy F (s)G(s) s ∈ DF ∩DG
15. f(k t), k ∈ R+ 1
k
F
( s
k
) s
k
∈ DF
Observac¸a˜o:
F (s) = L{f(t)} designa a Transformada de Laplace da func¸a˜o f(t) , DF designa o
domı´nio de F e U(t− a) representa a func¸a˜o de Heaviside.