Tabla de Transformadas de Laplace

Tabla de Transformadas de Laplace
1
Tabla de Transformadas de Laplace
f (t )
F ( s ) = L { f (t )}
1
1
s
1
s2
n!
s n +1
t
tn
t
−1
π
2
s
t
1
π
2
3
tα
∫
t
0
∫
t
0
2s 2
Γ(α + 1)
α > −1
sα +1
1
f (t )
t
∫
f (τ )dτ
F (s)
s
F ( s )G ( s )
f (τ ) g (t − τ )dτ
∞
s
F (u )du
( f * g )(t )
F ( s )G ( s )
f (t − a ) µ (t − a )
e− as F ( s)
g (t ) µ (t − a )
e− as L{g (t + a)}
µ (t − a)
δ (t − a)
e − as
s
− as
e
δ (t − to )
e− to s
sen ( kt )
k
s + k2
Instituto Tecnológico de Chihuahua / C. Básicas
2
Amalia C. Aguirre Parres
Tabla de Transformadas de Laplace
2
cos ( kt )
s
s + k2
sen 2 ( kt )
2k 2
s ( s 2 + 4k 2 )
cos 2 ( kt )
s 2 + 2k 2
s ( s 2 + 4k 2 )
k
2
s − k2
s
2
s − k2
2
senh ( kt )
cos h ( kt )
senh 2 ( kt )
2k 2
s ( s 2 − 4k 2 )
cos h 2 ( kt )
eat f (t )
s 2 − 2k 2
s ( s 2 − 4k 2 )
F ( s − a)
f ´(t )
sF ( s ) − f (0)
f ( n ) (t )
s n F ( s ) − s n −1 f (0) − s n − 2 f ´(0) − ... − sf ( n − 2) (0) − f ( n −1) (0)
t n f (t )
1
f (t )
t
eat
tn
eat t n
eat − ebt
ae at − bebt
eat sen ( kt )
Instituto Tecnológico de Chihuahua / C. Básicas
(−1) n F n ( s ) o bien (−1) n
∫
t
0
dn
F (s)
ds n
f (τ )dτ
1
s−a
n!
s n +1
n!
( s − a )n +1
( a − b)
( s − a ) − ( s − b)
(a − b) s
( s − a ) − ( s − b)
k
( s − a)2 + k 2
Amalia C. Aguirre Parres
Tabla de Transformadas de Laplace
eat cos kt
eat senh ( kt )
eat cos h ( kt )
e at − ebt
t
2 1 − cos ( kt ) 
t
2 [1 − cosh kt ]
t
sen(at )
t
sen(at ) cos(bt )
t
f (t ) periodo T
Instituto Tecnológico de Chihuahua / C. Básicas
3
s−a
( s − a)2 + k 2
k
( s − a)2 − k 2
s−a
( s − a)2 − k 2
s−a
ln 

 s−b
 s2 + k 2 
ln 

2
 s

 s2 − k 2 
ln 

2
 s

a
arctan  
s
1
a+b 1
a−b
arctan 
 + arctan 

2
 s  2
 s 
T
1
e st f (t )dt
sT ∫0
1− e
Amalia C. Aguirre Parres