Question
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 ¢, as shown in the figure. For the system to be critically damped, the ratio c/√(km) should be
Options :
2
4
Answer :
Solution :
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 “O”; ∑ M0 = 0
Now, moment of inertia of rod about the center of the rod is
Ic = mL²/12
Now, moment of inertia of rod about the center of the rod is
As we know that for critical dumping, the root of the quadratic equation should be real and equal.
∴ B − 4AC = 0
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