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A slender uniform rigid bar of mass m is hinged at O and supported by two springs, with stiffnesses 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/√km should be
  • a)
    4
  • b)
    2
  • c)
    4√7
  • d)
    2√7
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A slender uniform rigid bar of mass m is hinged at O and supported by ...
 When System is critically Damped
Suppose that we apply a external force downward at horizontal road at spring constant 3K and leave it freely for to and fro motion.
Therefore, moment about point

Now, moment of inertia of rod about the center of the rod is
And moment of inertia about the hinged point is I0=
As we know that for critical dumping, the root of the quadratic equation should be real and equal.

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A slender uniform rigid bar of mass m is hinged at O and supported by two springs, with stiffnesses 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/√km should bea)4b)2c)4√7d)2√7Correct answer is option 'C'. Can you explain this answer?
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