GATE ME 2019 Set 1 — Question 53
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Theory of Machines & Vibrations → Free Vibration → Undamped Free Vibration
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Question
A uniform thin disk of mass and radius is kept on a surface as shown in the figure. A spring of stiffness is connected to the disk center and another spring of stiffness is connected at point just above point on the circumference of the disk. Initially, both the springs are unstretched. Assume pure rolling of the disk. For small disturbance from the equilibrium, the natural frequency of vibration of the system is ______ (round off to one decimal place).
Correct answer
23 to 24
Solution
1.Given Data:
- Mass of disk,
- Radius of disk,
- Stiffness (at center )
- Stiffness (at point , distance from contact point)
For pure rolling, the instantaneous center of rotation (ICR) is the point of contact with the ground.
3.Equation of Motion:
Let the disk rotate by a small angle . - Displacement of center :
- Displacement of point :
Differentiating with respect to time :
4.Natural Frequency:
Rounding to one decimal place, we get .Continue learning with Success Tracker
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