Tabela de Transformadas de Laplace

Prévia do material em texto

0462 - Matema´tica Aplicada a` Engenharia Ele´trica
TRANSFORMADAS DE LAPLACE
L{f(t)} = F (s) =
∫ ∞
0
f(t)e−stdt
f(t) L{f(t)} = F (s) Se Enta˜o
K
K
s
s > 0 L{f(t)} = F (s) L{eatf(t)} = F (s− a)
tn
n!
sn+1
s > 0 L{f(t)} = F (s) L{f ′(t)} = sF (s)− f(0)
eat
1
s− a s > a L{f(t)} = F (s) L{f
′′(t)} = s2F (s)− sf(0)− f ′(0)
sin at
a
s2 + a2
s > 0 L{f(t)} = F (s) L
{∫ t
0
f(u)du
}
=
F (s)
s
cos at
s
s2 + a2
s > 0 L{f(t)} = F (s) L{tnf(t)} = (−1)n d
n
dsn
F (s)
sinh at
a
s2 − a2 s > |a| L{f(t)} = F (s) L{f(at)} =
1
a
F
(
s
a
)
cosh at
s
s2 − a2 s > |a| L{f(t)} = F (s) L{f(t− a)} = e
−asF (s)
u(t)
1
s
s > 0
δ(t) 1
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