GATE ME 2014 Set 1 — Question 48
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Theory of Machines & Vibrations → Free Vibration → Undamped Free Vibration
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Question
A rigid uniform rod of length and mass is hinged at such that , . Ends and are supported by springs of spring constant . The natural frequency of the system is given by
Correct answer
(D) √((5k)/(m))
Solution
Using the torque method for small angular displacement about the hinge :
Using parallel axis theorem: .
The restoring forces are and .
.
1.Moment of Inertia about C ():
The center of gravity is at from . The distance .Using parallel axis theorem: .
2.Restoring Torque ():
For a small rotation , the displacement at is and at is .The restoring forces are and .
.
3.Equation of Motion:
.4.Natural Frequency ():
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