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.