Correct Answer - Option 4 : 6

__Concept:__

The transfer function of the standard second-order system is:

\(TF = \frac{{C\left( s \right)}}{{R\left( s \right)}} = \frac{{\omega _n^2}}{{{s^2} + 2\zeta {\omega _n}s + \omega _n^2}}\)

ζ is the damping ratio

ωn is the natural frequency

Characteristic equation: \({s^2} + 2\zeta {\omega _n} + \omega _n^2\)

Roots of the characteristic equation are: \( - \zeta {\omega _n} + j{\omega _n}\sqrt {1 - {\zeta ^2}} = - \alpha \pm j{\omega _d}\)

α is the damping factor

__Calculation:__

Transfer function \(G\left( s \right) = \frac{{36}}{{{s^2} + 4.2s + 36}}\)

By comparing the above transfer function with the standard second-order system,

\(\omega _n^2 = 36 \Rightarrow {\omega _n} = 6\)