Transformadas de Laplace

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Tabla de Transformadas de Laplace 1 
Instituto Tecnológico de Chihuahua / C. Básicas Amalia C. Aguirre Parres 
Tabla de Transformadas de Laplace 
 
 
( )f t ( ) { ( )}F s f t= L 
1 1
s
 
t 
2
1
s
 
nt 
1
!
n
n
s + 
1
2t− 
s
π 
1
2t 
3
22s
π 
tα 
1
( 1) 1
sα
α α+
Γ + > − 
1 ( )f t
t
 ( )
s
F u du
∞
∫ 
0
( )
t
f dτ τ∫ ( )F s
s
 
0
( ) ( )
t
f g t dτ τ τ−∫ ( ) ( )F s G s 
( * )( )f g t ( ) ( )F s G s 
( ) ( )f t a t aµ− − ( )ase F s− 
( ) ( )g t t aµ − { ( )}ase g t a− +L 
( )t aµ − ase
s
−
 
( )t aδ − ase− 
( )ot tδ − ot se− 
( )sen kt 
2 2
k
s k+
 
Tabla de Transformadas de Laplace 2 
Instituto Tecnológico de Chihuahua / C. Básicas Amalia C. Aguirre Parres 
( )cos kt 
2 2
s
s k+
 
( )2sen kt 2
2 2
2
( 4 )
k
s s k+
 
( )2cos kt 2 2
2 2
2
( 4 )
s k
s s k
+
+
 
( )senh kt 
2 2
k
s k−
 
( )cosh kt 
2 2
s
s k−
 
( )2senh kt 2
2 2
2
( 4 )
k
s s k−
 
( )2cosh kt 2 2
2 2
2
( 4 )
s k
s s k
−
−
 
( )ate f t ( )F s a− 
(́ )f t ( ) (0)sF s f− 
( ) ( )nf t 1 2 ( 2) ( 1)( ) (0) (́0) ... (0) (0)n n n n ns F s s f s f sf f− − − −− − − − − 
( )nt f t 
( 1) ( )n nF s− o bien ( 1) ( )
n
n
n
d F s
ds
− 
1 ( )f t
t
 
0
( )
t
f dτ τ∫ 
ate 1
s a−
 
nt 
1
!
n
n
s + 
at ne t 
1
!
( )n
n
s a +−
 
at bte e− ( )
( ) ( )
a b
s a s b
−
− − −
 
at btae be− ( )
( ) ( )
a b s
s a s b
−
− − −
 
( )ate sen kt 
2 2( )
k
s a k− +
 
Tabla de Transformadas de Laplace 3 
Instituto Tecnológico de Chihuahua / C. Básicas Amalia C. Aguirre Parres 
cosate kt 
2 2( )
s a
s a k
−
− +
 
( )ate senh kt 
2 2( )
k
s a k− −
 
( )cosate h kt 
2 2( )
s a
s a k
−
− −
 
at bte e
t
− ln s a
s b
− 
 − 
 
( )2 1 cos kt
t
−   
2 2
2ln s k
s
 +
 
 
 
[ ]2 1 cosh kt
t
−
 
2 2
2ln s k
s
 −
 
 
 
( )sen at
t
 arctan a
s
 
 
 
 
( ) cos( )sen at bt
t
 1 1arctan arctan
2 2
a b a b
s s
+ −   +   
   
 
( ) periodo Tf t 
0
1 ( )
1
T st
sT e f t dt
e− ∫ 
 
	Tabla de Transformadas de Laplace