Laplace
3
APE-21 APÉNDICE III TRANSFORMADAS DE LAPLACE f (t) 1. 1 2. t 3. t n n un entero positivo 4. t 1/2 5. t 1/2 6. t a 7. sen kt 8. cos kt 9. sen 2 kt 10. cos 2 kt 11. e at 12. senh kt 13. cosh kt 14. senh 2 kt 15. cosh 2 kt 16. te at 17. t n e at n un entero positivo n! (s a) n 1 , 1 (s a) 2 s 2 2 k 2 s (s 2 4 k 2 ) 2 k 2 s (s 2 4 k 2 ) s s 2 k 2 k s 2 k 2 1 s a s 2 2k 2 s (s 2 4 k 2 ) 2k 2 s (s 2 4 k 2 ) s s 2 k 2 k s 2 k 2 ( 1) s 1 , a 1 1 2 s 3/2 B s n! s n 1 , 1 s 2 1 s { f (t)} F(s) www.elsolucionario.net www.elsolucionario.net
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transformadas de LAPLACE
Transcript of Laplace
APE-21
APÉNDICE III
TRANSFORMADAS DE LAPLACE
f (t)
1. 1
2. t
3. tn n un entero positivo
4. t 1/2
5. t1/2
6. ta
7. senkt
8. cos kt
9. sen2 kt
10. cos2 kt
11. eat
12. senh kt
13. cosh kt
14. senh2kt
15. cosh2kt
16. teat
17. tn eat n un entero positivon!
(s a)n 1 ,
1
(s a)2
s2 2k2
s(s2 4k2)
2k2
s(s2 4k2)
s
s2 k2
k
s2 k2
1
s a
s2 2k2
s(s2 4k2)
2k2
s(s2 4k2)
s
s2 k2
k
s2 k2
( 1)
s 1 , a 1
1
2s3/2
B s
n!
sn 1 ,
1
s2
1
s
{ f (t)} F(s)
08243_12_appendixIII.indd 21 6/4/09 12:37:12 PM
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APE-22 APÉNDICE III TRANSFORMADAS DE LAPLACE
f (t)
18. eat senkt
19. eat cos kt
20. eat senhkt
21. eat cosh kt
22. t senkt
23. t cos kt
24. senkt kt cos kt
25. senkt kt cos kt
26. t senhkt
27. t cosh kt
28.
29.
30. 1 cos kt
31. kt senkt
32.
33.
34. senkt senhkt
35. senkt cosh kt
36. cos kt senhkt
37. cos kt cosh kts3
s4 4k4
k(s2 2k2)
s4 4k4
k(s2 2k2)
s4 4k4
2k2s
s4 4k4
s
(s2 a2)(s2 b2)
cos bt cos at
a2 b2
1
(s2 a2)(s2 b2)
a sen bt b sen at
ab (a2 b2)
k3
s2(s2 k2)
k2
s(s2 k2)
s
(s a)(s b)
aeat bebt
a b
1
(s a)(s b)
eat ebt
a b
s2 k2
(s2 k2)2
2ks
(s2 k2)2
2k3
(s2 k2)2
2ks2
(s2 k2)2
s2 k2
(s2 k2)2
2ks
(s2 k2)2
s a
(s a)2 k2
k
(s a)2 k2
s a
(s a)2 k2
k
(s a)2 k2
{ f (t)} F(s)
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APÉNDICE III TRANSFORMADAS DE LAPLACE APE-23
f (t)
38. J0(kt)
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50. eat f (t) F(s a)
51.
52. e asF(s)
53. e as
54. f (n)(t)
55. tn f (t)
56. F(s)G(s)
57. d(t 1)
58. d(t t0) e st0
t
0f ( )g(t ) d
( 1)ndn
dsnF(s)
snF(s) s(n 1) f (0) f (n 1)(0)
{ g(t a)}g(t) (t a)
f (t a) (t a)
e as
s(t a)
erfca
21t
be a1s
s(1s b)eabeb
2 terfc b1ta
21t
e a1s
1s(1s b)eabeb
2t erfc b1ta
21t
e a1s
s1s2B
te a2/4t a erfc
a
21t
e a1s
serfc
a
21t
e a1sa
21 t3e a2/4t
e a1s
1s
1
1 te a2 /4t
1
2 arctan
a b
s
1
2 arctan
a b
s
senat cos bt
t
arctana
s
senat
t
lns2 k2
s2
2(1 cosh kt)
t
lns2 k2
s2
2(1 cos kt)
t
lns a
s b
ebt eat
t
1
1s2 k2
{ f (t)} F(s)
08243_12_appendixIII.indd 23 6/4/09 12:37:13 PM
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