Tabla de transformadas de Laplace. PDF

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Tabla de transformadas de Laplace....

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TABLA DE TRANSFORMADAS DE LAPLACE

t n,

f (t )

F (s )

f (t )

1

1 s

t  sen kt

n!

t  cos kt

n  1,2,3  s

2 ks

s s

 s

sen kt  kt  cos kt

1 sa

sen kt  kt  cos kt

t

sen kt

s

s k

t e

e

(s  at

e

a )2



2

2

 k2



2

k2

(s  a )2  k 2



a sen bt  b sen at

a b

s a

cos kt



s2 s2  k2 1

2

(s  a ) k

sen kt

 k2

kt  sen kt

2

n 1

at

2

k3

ab  a 2  b 2

n!

n  1,2,3 

2





s

2

cos bt  cos at

s k



s s2  k 2



2

s 2

n at

 k2



k 2

2

k2

2

s2  k 2

cosh kt

2

1 cos kt

s k



2ks 2

s

k

senh kt

 k2

2 k3

s

2

cos kt

2

s2  k 2

n 1

1

e at

F (s )







s



1 e at  e bt  b a



 a2  s2  b2



s

2

1 1  e  at a



2

2



 a  s 2  b2



1 s(s  a )



1 be bt  ae at b a

1 ( s  a)( s  b)



s (s  a )(s  b )

Funciones hiperbólicas: senh x 

ex  e  x 2

cosh x 

e x  e x 2

tgh x 

e x  e x x

e e

x

cosh 2 x  senh 2 x  1 senh(2 x )  2 senh x  cosh x cosh( 2 x)  senh 2 x  cosh 2 x

M09_Laplace tabla - 1

6.3 ALGUNAS TRANSFORMADAS INVERSAS ÚTILES

F (s )

f (t ) 1

1 s 1

t n 1 , (n  1)!

n

s 1

eat

s a 1

t n 1 at e ( n  1)!

n

(s  a ) 1 2

2

2

2

1 sen bt b

s b s

cos bt

s b Cs  D

(s 

a )2

b2

 Cs  D

(s  a )

2

n  1,2,3 





2 b2

Ceat cos bt 

Ca  D at e sen bt b

C at Ca  D at e  sen bt  bt cos bt  e t sen bt  2b 2 b3

M09_Laplace tabla - 2...