Higher Engineering Mathematics

644 LAPLACE TRANSFORMS

− 4 − 3 − 20 − 1123 σ

jω

j

−j

Figure 66.2

Now try the following exercise.

Exercise 237 Further problems on poles

and zeros

1. Determine for the transfer function:

R(s)=

50 (s+4)

s(s+2)(s^2 − 8 s+25)

(a) the zero and (b) the poles. Show the poles

and zeros on a pole-zero diagram.

[

(a)s=− 4 (b)s=0,s=−2,

s= 4 +j3,s= 4 −j 3

]

2. Determine the poles and zeros for the func-

tion: F(s)=

(s−1)(s+2)

(s+3)(s^2 − 2 s+5)

and plot

them on a pole-zero map.

[

poles ats=−3,s= 1 +j2,s= 1 −j2,

zeros ats=+1,s=− 2

]

3. For the functionG(s)=

s− 1

(s+2)(s^2 + 2 s+5)

determine the poles and zeros and show them

on a pole-zero diagram.

[

poles ats=−2,s=− 1 +j2,

s=− 1 −j2,

zero ats= 1

]

4. Find the poles and zeros for the transfer func-

tion:H(s)=

s^2 − 5 s− 6

s(s^2 +4)

and plot the results

in the s-plane.

[

poles ats=0,s=+j2,s=−j2,

zeros ats=−1,s= 6

]