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GATE2019 ME-2: 32

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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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Arjun asked Feb 9, 2019
GATE2019 ME-1: 6
The natural frequencies corresponding to the spring-mass systems $I$ and $II$ are $\omega_1$ and $\omega_{II}$, respectively. The ratio $\dfrac{\omega_I}{\omega_{II}}$ is $\dfrac{1}{4} \\$ $\dfrac{1}{2} \\$ $2 \\$ $4$
The natural frequencies corresponding to the spring-mass systems $I$ and $II$ are $\omega_1$ and $\omega_{II}$, respectively. The ratio $\dfrac{\omega_I}{\omega_{II}}$ is...
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