Tabela de Laplace - Unicampketty/ensino/ma311/TabelaLaplace.pdf · Tabela de Laplace f(t) F(s) 1 1...
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Tabela de Laplace f (t) F (s) 1 1 s e at 1 s - a t n n! s n+1 t a Γ(a + 1) s a+1 sen at a s 2 + a 2 cos at s s 2 + a 2 senh at a s 2 - a 2 cosh at s s 2 - a 2 e at sen bt b (s - a) 2 + b 2 e at cos bt (s - a) (s - a) 2 + b 2 t n e at n! (s - a) n+1 f (t) F (s) u c (t)= u(t - c) e -cs s u c (t)f (t - c) e -cs F (s) e ct f (t) F (s - c) f (ct) 1 c F s c Z t 0 f (t - τ )g (τ )dτ F (s)G(s) δ c (t)= δ (t - c) e -cs f (n) (t) s n F (s) - s n-1 f (0) - ... - f (n-1) (0) Z t 0 f (τ )dτ F (s) s f (t) t Z ∞ s F (σ)dσ (-t) n f (t) F (n) (s) f (t), per´ ıodo p 1 1 - e -ps Z p 0 e -st f (t)dt 1
Transcript of Tabela de Laplace - Unicampketty/ensino/ma311/TabelaLaplace.pdf · Tabela de Laplace f(t) F(s) 1 1...
Tabela de Laplace
f(t) F (s)
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s
eat 1
s− a
tnn!
sn+1
taΓ(a+ 1)
sa+1
sen ata
s2 + a2
cos ats
s2 + a2
senh ata
s2 − a2
cosh ats
s2 − a2
eatsen btb
(s− a)2 + b2
eat cos bt(s− a)
(s− a)2 + b2
tneat n!
(s− a)n+1
f(t) F (s)
uc(t) = u(t− c) e−cs
s
uc(t)f(t− c) e−csF (s)
ectf(t) F (s− c)
f(ct)1
cF(sc
)∫ t
0f(t− τ)g(τ)dτ F (s)G(s)
δc(t) = δ(t− c) e−cs
f (n)(t) snF (s)− sn−1f(0)− . . .− f (n−1)(0)∫ t
0f(τ)dτ
F (s)
s
f(t)
t
∫ ∞s
F (σ)dσ
(−t)nf(t) F (n)(s)
f(t), perıodo p1
1− e−ps
∫ p
0e−stf(t)dt
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