PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

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