# In the standard form of closed loop transfer function of second order system is given by C(s)/R(s)= ω2n /s2+2ςωns+ω2n The damping ratio ζ = 0, then th

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In the standard form of closed loop transfer function of second order system is given by C(s)/R(s)= ω2n /s2+2ςωns+ω2n The damping ratio ζ = 0, then the system is
1. undamped system
2. under damped system
3. critically damped system
4. over damped system

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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

 ζ Nature ζ = 0 Undamped 0 < ζ < 1 Underdamped ζ = 1 Critically damped ζ > 1 Overdamped