A slender uniform rigid bar of mass $m$ is hinged at $O$ and supported by two springs, with stiffness, $3k$ and $k$ and a damper with damping coefficient $c$, as shown in the figure. For the system to be critically damped, the ratio $c/\sqrt{km}$ should be
1. $2$
2. $4$
3. $2 \sqrt{7}$
4. $4 \sqrt{7}$