Tabela de Transformadas de Laplace
Fun¸c˜ao Transformada de Laplace Dom´ınio
1.k, constante k
ss > 0
2.tn, n = 1,2,3, ... n!
sn+1 s > 0
3.t−1/2rπ
ss > 0
4.ek t 1
s−ks>k
5. sin (k t)k
s2+k2s > 0
6. cos (k t)s
s2+k2s > 0
7. sinh (k t)k
s2−k2s > |k|
8. cosh (k t)s
s2−k2s > |k|
9.ek t f(t)F(s−k) = L {f(t)}s→s−ks−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.tnf(t), n = 1,2, ... (−1)ndnF(s)
d sn
13.f(n)(t), n = 1,2, ... snF(s)−sn−1f(0) −sn−2f0(0) −... −f(n−1)(0) s∈DF
14.Zt
0
f(y)g(t−y)dy F (s)G(s)s∈DF∩DG
15.f(k t), k ∈R+1
kFs
ks
k∈DF
Observa¸c˜ao:
F(s) = L {f(t)}designa a Transformada de Laplace da fun¸c˜ao f(t) , DFdesigna o
dom´ınio de FeU(t−a) representa a fun¸c˜ao de Heaviside.
