GATE ME 2015 Set 1 — Question 48
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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) [figure]
Solution
Let the rod rotate by a small angle about the pivot.
The spring force is .
The restoring moment about the pivot is .
The acceleration is .
The inertia force is .
The inertia moment about the pivot is .
1.Restoring Moment from Spring:
The deflection of the spring is .The spring force is .
The restoring moment about the pivot is .
2.Inertia Moment from Mass:
The displacement of the mass is .The acceleration is .
The inertia force is .
The inertia moment about the pivot is .
3.Equation of Motion:
Summing moments about the pivot:Dividing by :The natural frequency is:Substituting and :Thus, the correct option is (D).Continue learning with Success Tracker
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