Tabela transformada de Laplace

Prévia do material em texto

Tabla de Transformadas de Laplace
L {f (t)} = ∫ ∞0 e−s t f (t) dt
f(t) F (s) f(t) F (s)
1. 1
1
s
2. tn, n = 1, 2, 3, ..
n!
sn+1
3. tα, −1 < α Γ(α+ 1)
sα+1
4. ea t
1
s− a
5. tn ea t, n = 1, 2, 3, ..
n!
(s− a)n+1 6. sin (ω t)
ω
s2 + ω2
7. cos (ω t)
s
s2 + ω2
8. sinh (ω t)
ω
s2 − ω2
9. cosh (ω t)
s
s2 − ω2 10. e
a t sin (ω t)
ω
(s− a)2 + ω2
11. ea t cos (ω t)
s− a
(s− a)2 + ω2 12. t sin (ω t)
2ω s
(s2 + ω2)2
13. t cos (ω t)
s2 − ω2
(s2 + ω2)2
14. sin (ω t)− ω t cos (ω t) 2ω
3
(s2 + ω2)2
15. sin (ω t) + ω t cos (ω t)
2ω s2
(s2 + ω2)2
16.
1
a− b
(
ea t − eb t
) 1
(s− a) (s− b)
17.
1
a− b
(
a ea t − b eb t
) s
(s− a) (s− b) 18.
1
a2
(1− cos (a t)) 1
s (s2 + a2)
19.
1
a3
(a t− sin (a t)) 1
s2 (s2 + a2)
20. f(t) + g(t) F (s) +G(s)
21. c f(t) c F (s) 22. f ′(t) s F (s)− f(0)
23. f ′′(t) s2 F (s)− s f(0)− f ′(0) 24. f (n)(t) sn F (s)− sn−1 f(0)− · · · − f (n−1)(0)
25. ea t f(t) F (s− a) 26. tn f(t) (−1)n d
n
dsn
F (s)
27. Ua(t) = U(t− a) e
−a s
s
28. f(t− a)Ua(t) e−a s F (s)
29. f ∗ g =
∫ t
0
f(t− σ)g(σ)dσ F (s)G(s) 30. δ(t− c) e−c s
31. f(t+ T ) = f(t)
∫ T
0
e−s t f(t) dt
1− e−s T 32.
∫ t
0
f(σ) dσ
1
s
F (s)
33.
f(t)
t
∫ +∞
s
F (σ) dσ 34. f(a t)
1
a
F
(
s
a
)
lim
s→+∞ s F (s) = f(0) lims→0+
s F (s) = lim
t→+∞ f(t)
(c) Departamento de Matema´ticas. ITESM, Campus Monterrey
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