# Gate 2016 EE – Set 2 – Question 50

Second order characteristic equation $$\Rightarrow S^{2}+2\delta \omega _{n}S+\omega _{n}^{2}=0$$
where $$\delta =0.5 and \omega _{n}=10$$

The equation now becomes, $$S^{2}+(2)(0.5)(10)S+100=0$$

$$S^{2}+10S+100=0$$

Check with the given options, which results in the input value of 1.02

Option B checks since, DC gain = $$\frac{102}{\omega _{n}^{2}}=\frac{102}{100}=1.02$$