Correct Answer - Option 3 : 0.707
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:
Given poles are: s = -2 ± j2
By comparing with the standard second-order system,
ζωn = 2
\({\omega _n}\sqrt {1 - {\zeta ^2}} = 2\)
From the above two equations, \(\zeta = \sqrt {1 - {\zeta ^2}} \)
⇒ ζ = 0.707
