# The casual system represented by $G(s) = \dfrac{9}{{({s^2} + 6s + 9)}}$

The casual system represented by $G(s) = \dfrac{9}{{({s^2} + 6s + 9)}}$

### Right Answer is: Critically damped

#### SOLUTION

$G(s) = \dfrac{9}{{({s^2} + 6s + 9)}}$

Comparing the above equation with standard second-order closed-loop transfer function

$G(s) = \dfrac{{\omega _n^2}}{{({s^2} + 2\xi {\omega _n}s + \omega _n^2)}}$

∴ 2ξωn = 6

ω2n = 9  = ωn = 3 rad/sec

∵ 2ξωn = 6

2ξ × 3 = 6

ξ = 1

Hence the system is critically damped.

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