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

- $2$
- $4$
- $2 \sqrt{7}$
- $4 \sqrt{7}$