PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Fourier and Laplace 453

c. cos(3w)

d. 2/(jw + 2)

e. 3/(jw + 2)^2

f. −1/w^2

P.4.25 Using the MATLAB symbolic toolbox, repeat P.4.24.

P.4.26 Obtain the following ILTs using Table 4.2, and indicate the Laplace properties used

in the process:

a. (s + 3)/(s^2 + 4 s + 5)

b. δ(s)

c. cos(3s)

d. (2s^2 + 4 s + 4)/(s^2 + 3 s + 2)

e. s + 3/(s + 2)^2

f. −1/s^2

P. 4. 2 7 Ve r i f y t h a t f(t) and F(s) given as follows constitute a LT pair

ft e t te Fs

s

e

ss

tt

s

() sin( ) ()

()

 











3443

3

216

2

3

223

3

23





 ↔

P.4.28 Find the partial fraction expansion of each of the following functions:

a. 2s/(s^2 + 5s + 4)

b. (2s^2 + 1)/(s^2 + 5s + 4)

c. 2s/(s^2 + 6s + 8)

d. 2s/(s^2 + 1s + 1)

e. s^2 /(s^2 + 5s + 4)

f. s/(s^2 + 3s + 4)

P.4.29 Verify the following LT pairs:

a. ft t t Fs s e

s

s

()
cos( ) sin( ) () (
)



532432 512

9

2

 2



↔

b. ft t Fs

ss s

() sin () ()

()( )( )

 

5

22222

120

13 5

↔

c. ft t Fs

ss s s

() sin () ()

()()()



6

222222

720

246

↔

d. ft

t

t

Fs

s

s

()

sin ( )



() ln

(^22)  2
2

1

4

2

↔









P.4.30 Verify that the current i(t) shown in the circuit diagram of Figure 4.95 is given by

it I s

ss

() = £−^1 {}()= 2

50

 (^25)
assuming that all the initial conditions are zero.