Question

The $3-dB$ bandwidth of a typical second-order system with the transfer function
$\frac{C\left(s\right)}{R\left(s\right)}=\frac{{\omega }_n^2}{s^2+2\xi {\omega }_{n}s+{\omega }^{2}n},$ is given by

• A. ${\omega }_n\sqrt{1-2{\xi }^2}$
• B. ${\omega }_n\sqrt{(1-{\xi }^2)+\sqrt{{\xi }^4-{\xi }^2+1}}$
• C. ${\omega }_n\sqrt{(1-2{\xi }^2)+\sqrt{4{\xi }^4-4{\xi }^2+2}}$
• D. ${\omega }_n\sqrt{(1-2{\xi }^2)-\sqrt{4{\xi }^4-4{\xi }^2+2}}$

Answer 1

The correct option is C ${\omega }_n\sqrt{(1-2{\xi }^2)+\sqrt{4{\xi }^4-4{\xi }^2+2}}$

${\omega }_n\sqrt{(1-2{\xi }^2)+\sqrt{4{\xi }^4-4{\xi }^2+2}}$