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THE LAPLACE TRANSFORM METHOD

Time Domain (i) Ri + L di = L dt

[CHAP. 16

s-Domain (ii) RI(s) + L[_ i(0+) + sI(s)] = V(s) _

(iii) 5I(s) + (2.5× 10 3)[_2 +sI(s)]=

50 s

(classical methods) _8 10 + s s+2000 _ 1 =10 10L 1 s _ _ 1 (_8)L 1 = _ 8e 2000t s+2000

(iv) I(s)= (v) (vii) i(t) = 10 _ 8e

_2000t

(A)

(vi)

Table 16-1 Laplace Transform Pairs f ðtÞ

FðsÞ

1.

1

2.

t

3.

eat

4.

teat

5.

sin !t

6.

cos !t

1 s 1 s2 1 sþa 1 ðs þ aÞ2 ! s2 þ ! 2 s s2 þ ! 2

7.

sin ð!t þ Þ

s sin  þ ! cos  s2 þ ! 2

8.

cos ð!t þ Þ

9.

eat sin !t

10.

eat cos !t

11.

sinh !t

12.

cosh !t

sþa ðs þ aÞ2 þ !2 ! s2  ! 2 s s2  ! 2

13.

df dt

sFðsÞ  f ð0þ Þ

ðt

f ðÞ d

s cos   ! sin  s2 þ ! 2 ! ðs þ aÞ2 þ !2

FðsÞ s

14.

0

15.

f ðt  t1 Þ

et1 s FðsÞ

16.

c1 f1 ðtÞ þ c2 f2 ðtÞ ðt f1 ðÞ f2 ðt  Þ d

c1 F1 ðsÞ þ c2 F2 ðsÞ

17.

0

F1 ðsÞF2 ðsÞ

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An