Show that the magnitude (|G(j omega)|=frac{1}{sqrt{left[1-left(omega / omega_{n} ight)^{2} ight]^{2}+left(2 zeta omega / omega_{n} ight)^{2}}}) attains a

Show that the magnitude \(|G(j \omega)|=\frac{1}{\sqrt{\left[1-\left(\omega / \omega_{n}\right)^{2}\right]^{2}+\left(2 \zeta \omega / \omega_{n}\right)^{2}}}\) attains a maximum when

\[\frac{\omega}{\omega_{n}}=\sqrt{1-2 \zeta^{2}}\]