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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. $4 \sqrt{7}$
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