GATE ME 2015 Set 1 — Question 58
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Theory of Machines & Vibrations → Free Vibration → Undamped Free Vibration
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Question
Considering massless rigid rod and small oscillations, the natural frequency (in rad/s) of vibration of the system shown in the figure is
Correct answer
(D) √((400)/(4))
Solution
1.Let be the small angular displacement of the rod about the pivot.
2.The restoring torque from the spring is .
3.The moment of inertia of the mass about the pivot is .
4.The equation of motion is .
5.The natural frequency is .
6.Substituting the given values N/m and kg: rad/s.
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