Correct Answer - Option 4 : 5 rad/s and 0.60
Concept:
The characteristic equation of a 2nd order system can be represented as follows:
\( {\rm{\Delta }}s=s^2+2\zeta \omega_n s+\omega_n^2\)
Analysis:
Pole locations = -3 + j4 and -3 - j4
The characteristic equation can be written as:
\( {\rm{\Delta }}s = \left\{ {s - \left( { - 3 + j4} \right)} \right\}\left\{ {s - \left( { - 3 - j4} \right)} \right\} \)
\(= {\left( {s + 3} \right)^2} + {4^2} = {s^2} + 6s + 25\)
\( \omega _n^2 = 25 \Rightarrow {\omega _n} = 5\;rad/s \)
\(2\zeta {\omega _n} = 6 \)
\(\zeta = 0.6 \)