Page 9 - LAPLACE TRANSFORM

Table of Laplace Transform

Time domain function Frequency domain

No f(t) F(s)

-1
ƒ(t) = ʆ {F(s)} F(s) = ʆ {f(t)}
1 Unit Impulse ẟ(t) 1

1
2 Unit step u(t)
s
1
3 t
s 2
t n−1 1
4 (n=1,2,3….)
(n−1)! s n
n!
n
5 t (n=1,2,3….)
s n+1
1
6 e −at
(s + a)
1
7 te −at
(s + a) 2

1 n−1 −at 1
8 t e (n=1,2,3….)
(n−1)! (s + a) n
n!
n
9 t e −at
(s + a) n+1
ꞷ
10 sin ꞷt
2
s + ꞷ 2
s
11 cos ꞷt
s + ꞷ 2
2
ꞷ
12
2
e −at sin ꞷt (s + a) + ꞷ 2
(s + a)
13
2
e −at cos ꞷt (s + a) + ꞷ 2
a
14 sinh at
2
s − a 2
s
15 cosh at
2
s − a 2
2as
16 t sin at
2
2 2
( s + a )
2
s − a 2
17 t cos at
2 2
2
( s + a )

3