GATE ECE 1994 | Question 1.5

Question

The $3-d \mathrm{B}$ bandwidth of a typical second-order system with the transfer function
$\frac{\mathrm{C}(s)}{\mathrm{R}(s)}=\frac{w_{n}^{2}}{s^{2} \mathrm{t}+2 x w_{n} s+w_{n}^{2}}$ is given by

• A. $\omega_{n}=\sqrt{1-2 \xi^{2}}$
• B. $\omega_{n}=\sqrt{\left.1-2 \xi^{2}\right)+\sqrt{\xi^{4}-\xi^{2}+1}}$
• C. $\omega_{n}=\sqrt{\left.1-2 \xi^{2}\right)+\sqrt{4 \xi^{4}-4 \xi^{2}+2}}$
• D. $\omega_{n}=\sqrt{\left.1-2 \xi^{2}\right)+\sqrt{4 \xi^{4}-4 \xi^{2}+2}}$