Correct Answer - Option 1 : undamped system
The general expression of the transfer function of the standard second-order system is:
\(TF = \frac{{C\left( s \right)}}{{R\left( s \right)}} = \frac{{\omega _n^2}}{{{s^2} + 2\zeta {\omega _n}s + \omega _n^2}}\)
Where,
ζ is the damping ratio
ωn is the undamped natural frequency
Characteristic equation: \({s^2} + 2\zeta {\omega _n} + \omega _n^2 = 0\)
The 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
The nature of the system is described by its ‘ζ’ value
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ζ
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Nature
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ζ = 0
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Undamped
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0 < ζ < 1
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Underdamped
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ζ = 1
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Critically damped
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ζ > 1
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Overdamped
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