Fourier and Laplace 353
then
Fs
ss s
s
s
()
() ( )
()
52
3
10 3
3
52
++^222722
+
++
b. Example (#2)
Let
Fs
ss s
()
10 20 30
(^23)
Find f(t).
ANALYTICAL Solution
(From Table 4.2)
ft Fs ft
ss s
() £() ()
11
2
10 20 30
3
[] £ {}
then
f(t) = 10 + 20 t u(t) + 30 e−^3 t u(t)
c. Example (#3)
Let
Fs
s
s
()
830
(^225)
Find f(t).
ANALYTICAL Solution
(From Table 4.2)
Fs
s
ss
()
8
5
6
5
(^22225)
then
f(t) = £−^1 [F(s)] = 8 cos( 5 t) u(t) + 6 sin( 5 t) u(t)
d. Example (#4)
Let
Ys
s
ss s
()
()( )
410
(^12)
Find y(t).
ANALYTICAL Solution
Ys
A
s
B
s
C
s
()
12