GATE ME 2019 Set 2 — Question 42
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Theory of Machines & Vibrations → Free Vibration → Damped Free Vibration
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Question
A slender uniform rigid bar of mass is hinged at O and supported by two springs, with stiffnesses and , and a damper with damping coefficient , as shown in the figure. For the system to be critically damped, the ratio should be
Correct answer
(D) 4√(7)
Solution
1.Moment of Inertia about hinge O:
The hinge O is at from the left end. Using the parallel axis theorem:2.Equivalent Torsional Stiffness ():
Spring is at distance from O. Spring is at distance from O.3.Equivalent Torsional Damping ():
The damper is at from the left end, which is from O.4.Critical Damping Condition:
For critical damping, :Thus, option (D) is correct.Continue learning with Success Tracker
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