Modern Control Engineering

Appendix A / Laplace Transform Tables 863

f(t) F(s)

1 Unit impulse d(t) 1

2 Unit step 1(t)

3 t

4

5 tn (n=1, 2, 3,p)

6 e–at

7 te–at

8

9 tne–at (n=1, 2, 3,p)

10 sinvt

11 cosvt

12 sinhvt

13 coshvt

14

15

16

17

1

s(s+a)(s+b)

1

ab

c 1 +

1

a-b

Abe-at-ae-btBd

s

(s+a)(s+b)

1

b-a

Abe-bt-ae-atB

1

(s+a)(s+b)

1

b-a

Ae-at-e-btB

1

s(s+a)

1

a

A 1 - e-atB

s

s^2 - v^2

v

s^2 - v^2

s

s^2 +v^2

v

s^2 +v^2

n!

(s+a)n+^1

1

(s+a)n

1

(n-1)!

tn-^1 e-at (n=1, 2, 3,p)

1

(s+a)^2

1

s+a

n!

sn+^1

1

sn

tn-^1

(n-1)!

(n=1, 2, 3,p)

1

s^2

1

s

Table A–1 Laplace Transform Pairs

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