GATE ME 2016 Set 2 — Question 47
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Theory of Machines & Vibrations → Free Vibration → Undamped Free Vibration
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Question
The system shown in the figure consists of block A of mass 5 kg connected to a spring through a massless rope passing over pulley B of radius and mass 20 kg. The spring constant is 1500 N/m. If there is no slipping of the rope over the pulley, the natural frequency of the system is_____________ rad/s.
Correct answer
9.9 to 10.1
Solution
The natural frequency of the system can be found using the energy method. The total energy is the sum of kinetic energy and potential energy .Since there is no slipping, . The mass moment of inertia of the pulley is .The potential energy is .For a conservative system, :The natural frequency is .Given kg, kg, and N/m: rad/s.
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