Correct Answer - Option 2 : √11 rad/sec
Analysis:
Given open-loop transfer function is:
\(G(s)H(s) = \frac{K}{{({s^3} + 6{s^2} + 11s + 6)}}\)
The characteristic equation is given by 1 + G(s)H(s) = 0
s3 + 6s2 + 11s + 6 + k = 0
By RH table
|
s3
|
1
|
11
|
|
s2
|
6
|
K + 6
|
|
s1
|
\(\frac{{66 - (k + 6)}}{{6}}\)
|
0
|
|
s0
|
K + 6
|
|
For k value put s1 row = 0
\(\frac{{66 - (k + 6)}}{{6}}\) = 0
k = 60
For ω value put s2 row = 0
6s2 + (k+6) = 0
-6ω2 + 66 = 0
ω2 = 11
ω = √11 rad/sec
