Modern Control Engineering

864 Appendix A / Laplace Transform Tables

18

19

20 e–atsinvt

21 e–atcosvt

22

23

24

25 1-cosvt

26 vt-sinvt

27 sinvt-vtcosvt

28

29 tcosvt

30

31

s^2

As^2 +v^2 B^2

1

2 v

(sinvt+vtcosvt)

s

As^2 +v^21 BAs^2 +v^22 B

1

v^22 - v^21

Acosv 1 t-cosv 2 tB Av^21 Zv^22 B

s^2 - v^2

As^2 +v^2 B^2

s

As^2 +v^2 B^2

1

2 v

tsinvt

2 v^3

As^2 +v^2 B^2

v^3

s^2 As^2 +v^2 B

v^2

sAs^2 +v^2 B

(0 6 z 6 1, 06 f 6 p2)

v^2 n

f=tan-^121 - z sAs^2 +^2 zvns^ +vn^2 B

2

z

1 -

1

21 - z^2

e-zvn^ tsin Avn 21 - z^2 t+fB

(0 6 z 6 1, 06 f 6 p2)

s

f=tan-^121 - z s^2 +^2 zvn^ s+vn^2

2

z

-

1

21 - z^2

e-zvn^ tsin Avn 21 - z^2 t-fB

v^2 n

s^2 + 2 zvn s+v^2 n

vn

21 - z^2

e-zvn^ tsinvn 21 - z^2 t (0 6 z 6 1)

s+a

(s+a)^2 +v^2

v

(s+a)^2 +v^2

1

s^2 (s+a)

1

a^2

Aat- 1 +e-atB

1

s(s+a)^2

1

a^2

A 1 - e-at-ate-atB

Table A–1 (continued)

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