solution

Code:
omg = 0.01:0.01:10000;
num = [20,0];den = [1,20,10000];
sys = tf(num,den);
figure(1),bode(omg,sys);grid on
Magnitude (dB)
Phase (deg)
0
-10
-20
-30
-40
90
45
0
-45
-90
10 1
Asymptote:
Bode Diagram
10 2
Frequency (rad/sec)
j20ω
H( jω)
=
( jω+ 10 − j99.5)( jω+ 10 + j99.5)
ω
j
j20ω
=
= 500
2
2
⎡ ω ω ⎤
10000 ⎢1− + j
⎛ ω ⎞ ω
10000 500
⎥ 1−
⎜ ⎟ + j
⎣ ⎦ ⎝100 ⎠ 500
From the expression, we see the frequency response have: zero at jω = 0 , a pair of
complex conjugate poles at jω =− 10 + j99.5
and jω = −10 − j99.5
.
(1). Magnitude asymptote
10 3