Transformada De Laplace

f (t)
1

H (t-)
2

TABLA DE TRANSFORMADA DE LAPLACE f (t) F (s)= L {f(t)} F (s)= L {f(t)} 12 1  s m! t m, m  e s s m 1
1 s  a a 2 s  a2
s 2 s  a2 a s2  a 2 s 2 s  a2
13

e

at

t m,
14

m 
m(m+1) s m 1

3

Senh at
4

t
15

f (t)

(1) m

dm F(s) ds m

Cosh at
5

t n-1
16

e

at( n  1)! (s  a ) n

Sen at
6

f (t-) H (t-)
17
t

e

 s

F(s)

Cos at
7

 f ( t )g()d
0

F (s). G(s)

18

e
8

at

f(t)

F (s-a)
19

t

 f ()d
0

F (s ) s

f (n) (t)
9sn F(s)-sn-1 f (0) – sn-2 f ’(0)-....-f n-1(0)
20

( t  a )
si f (t) = f (t + T)
21

e
1 1 e
 sT

as

f (kt)
10

1  s  F  k k

T

e
0

 st

f ( t )dt

f (t) t



si

 F(s)ds
se
22

t

(

B  A Sen  t ) 
t

As  B (s  ) 2  2

 Lim 
t 0

f (t) t

+
s 2 +a 2 - se

(ACost )

11

J n (at)





n

J 0 (at)

a n s 2 +a 2 1
s 2 +a 2

e


t

A B (sent  t cos t )
23
As  B
t

e

A tsen  t 2

s   

2

 2



2