Laplace

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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

Page 1: 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)

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Page 2: Laplace

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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Page 3: Laplace

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)

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