The transfer function of a system is
\[
G(s)=\frac{\omega_{n}^{2}}{s^{2}+2 \xi \omega_{n} s+\omega_{n}^{2}}
\]
Choose the range of $\xi$ and $\omega_{n}$ (in $\mathrm{rad} / \mathrm{s}$ ) from the following options such that the poles lie on the shaded region of the $s$-plane as shown in the figure.
$\xi \geq \frac{1}{2}$ and $\omega_{n} \geq 2$
$\xi \geq \frac{1}{4}$ and $\omega_{n} \geq 2$
$\xi \geq \frac{1}{2}$ and $\omega_{n} \geq \sqrt{3}$
$\xi \geq \frac{1}{4}$ and $\omega_{n} \geq \sqrt{3}$