Damping ratio and natural frequency 1.1

Ask

The transfer function of a system is $T(s)=\frac{5}{(s+3)(s+6)}$.The damping ratio and natural frequency are respectively

(a) 4.24,2.12 rad/s

(b) 2.12,4.24 rad/s

(c) 4.24,1.06 rad/s

(d) 1.06,4.24 rad/s

Answer is ( )

Concept

The transfer function of a system is $T(s) = \frac{5}{s^2 + 9s +18}$

Characteristic Eqn. $s^2 + 9s +18 = 0$ STANDARD Characteristic Eqn. $s^2 + 2\zeta\omega_n s + \omega_n^{2} = 0$

Comparing both Std & Characteristic Characteristic Eqn. gives $\omega_n^{2} = 18$

$2\zeta\omega_n = 9$ .On Solving , $\omega_n = 4.24$ rad/sec & $\zeta = 1.06$