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Automatic Control System.pdf


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Laplace Transform Table (cont.)

Time Function /(7)

Laplace Transform F(s)

2

4

1 — cos cont
2

s{s +co )
con J a2 + OJ2 sin(6>„/ + 9)
where 6 = t a n - ' (con/a)
W
" r-°" 1
*
nnf/.t t
<* + «5
\/ff2 + co2

COn
*-**rt

(5 + a) (j2 + ^ 2 )

A1

w h e r e # = t a n - (co„/a)
w2
J 2 + 2t;cons + co2
"'B

2

•4

"*"

———e

,/i

v-2 »

sina;„vJ

1

i

2

„-fa)„/oin,.

(rs\\

(G<1)

C '

'

?-&"'<\«{„hl^f\ & t +a)

s{s + 2t;cons + co )
wherefl^cos""" 1 ?

(f<l)

2

2
SO),,

_u>

s2 + 2£co„s + co2

r"to"'nnfa) \/l

»

wherefl = cos~ l £

s2(s2 + 2^cons + co2)

(?<1)

• W " " f ^ " ^ * ^ " " * ^ ^ 1 -f 2 , + ")
V

'

where* - tan" 1 ^

-I

fll

-5

/ 2

coj,{s + a)
s2 + 2$co„s + a>2

f2 f

O j-

1

1 ^
a - £con

,

(*<1)

.

t - ^ +
r
? ' - * * s m ( w „ \ / l - <2 / + 0)
v
7
«h tony/I-^
_l
2
where# = c o s ( 2 £ - l )
(f<l)