I have second order transfer function $$ G(s) = \frac{1.247}{s^2+9.76s+23.8}$$ G(s) is in the forward path of a unity feedback system.
How do I find the closed loop transfer function and damping constant from this? Now I know that the equation to find the closed loop transfer function is $$TF = \frac{G}{1+G}$$
If I use that here, I get $$TF = \frac{1.247}{s^2+9.76s+25.047}$$ and It is not in the form of a standard second order system which is $$TF = \frac{\omega_n^2}{s^2+2\delta\omega_ns+\omega_n^2}$$
That is, the numerator in TF is not 25.047. So How do I calculate damping ratio in this situation? Can I still take 25.047 as the square of natural frequency and equate that with the coefficient of s to find damping ratio?