Transformaty Laplace’a niektórych funkcji Funkcja f( t) Transformata F( s)
( t )
1
1(t)
1
s
kt
k
2
s
2
kt
k
3
2
s
kt n
k
n
n!
1
s
at
k
ke
s a
1
k
k
a
e
as
a
1
sin t
2
2
s
s
cos t
2
2
s
e at sin t 2
2
( s a )
s a
e at cos t 2
2
( s a )
t
1
a
1 e
s ( as 1) 2
1
a
1
te
a 2
2
( as 1)
t
t
e a e b
1
a b
( as 1)( bs 1) t
1
s
a
( a t ) e a 3
2
( as 1)
t
t
ae b be a s
ab ( a b ) ( as 1)( bs 1) t
b
bs 1
a
1 1
e
a
s ( as 1) 3
t
ae a be b 1
1
b a
s ( as 1)( bs 1) t
1
t a 1
(
a
e
)
2
s ( as 1)
t
2
k
e
n
k
n
2
sin (
1 t )
n
n
2
2
2
1
s
2
s
n
n
2
k
t
2
2
n
k 1
e
cos (
1 t )
sin (
1
t )
n
n
n
2
2
2
1
s ( s 2
s
)
n
n
a
2
t
a
2
de
cos
b
t
4
ds c
ad
c
2
a
2
s
as
b
t
a
2
2
e
sin
b
t
2
a
4
b
4
4