Tabela de Laplace
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6 Tabela de Transformadas de Laplace Transformadas de Laplace Elementares f (t) F (s)= L(f )(s) f (t) F (s)= L(f )(s) 1 1 s , para s> 0 e at 1 s - a , para s>a cos at s s 2 + a 2 , para s> 0 sen at a s 2 + a 2 , para s> 0 t n , para n ∈ Z + n! s n+1 , para s> 0 e at f (t) F (s - a) f (t) sF (s) - f (0) f (t) s 2 F (s) -sf (0) -f (0) t cos at s 2 - a 2 (s 2 + a 2 ) 2 , s> 0 t sen at 2as (s 2 + a 2 ) 2 , s> 0 sen at - at cos at 2a 3 (s 2 + a 2 ) 2 , s> 0 δ (t - t 0 ))(s) e -t 0 s , s> 0 u a (t)= 0, 0 ≤ t<a 1, t ≥ a e -as s , para s> 0 u a (t)f (t -a) e -as F (s) f (t)δ (t - t 0 ))(s) e -t 0 s f (t 0 ), s> 0 t 0 f (t - τ )g(τ )dτ F (s)G(s)
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Transcript of Tabela de Laplace
6 Tabela de Transformadas de Laplace
Transformadas de Laplace Elementares
f(t) F (s) = L(f)(s) f(t) F (s) = L(f)(s)
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s, para s > 0 eat
1
s − a, para s > a
cos ats
s2 + a2, para s > 0 sen at
a
s2 + a2, para s > 0
tn, para n ∈ Z+
n!
sn+1, para s > 0 eatf(t) F (s − a)
f ′(t) sF (s) − f(0) f ′′(t) s2F (s)−sf(0)−f ′(0)
t cos ats2 − a2
(s2 + a2)2, s > 0 t sen at
2as
(s2 + a2)2, s > 0
sen at − at cos at2a3
(s2 + a2)2, s > 0 δ(t − t0))(s) e−t0s, s > 0
ua(t) =
{
0, 0≤ t< a
1, t ≥ a
e−as
s, para s > 0 ua(t)f(t−a) e−asF (s)
f(t)δ(t − t0))(s) e−t0sf(t0), s > 0∫
t
0f(t − τ)g(τ)dτ F (s)G(s)
Tabela: Transformada de Laplace
11
s
eat1
s− a
tnn!
sn+1
senata
s2 + a2
cos ats
s2 + a2
senh ata
s2− a2
cosh ats
s2− a2
eatsenbtb
(s− a)2 + b2
eat cos bts− a
(s− a)2 + b2
tneatn!
(s− a)n+1
Uc(t)e−cs
s
Uc(t)f(t− c) e−csF (s)
ectf(t) F (s− c)
f(ct)1
cF
(s
c
)
∫
t
0
f(t− τ)g(τ)dτ F (s)G(s)
δ(t− c) e−cs
f (n)(t) snF (s)− s(n−1)f(0)− . . .− f (n−1)(0)
(−t)nf(t) F (n)(s)
