GATE ME 2021 Set 2 — Question 44
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Theory of Machines & Vibrations → Free Vibration → SDOF Free Vibration
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Question
Consider the system shown in the figure. A rope goes over a pulley. A mass, , is hanging from the rope. A spring of stiffness, , is attached at one end of the rope. Assume rope is inextensible, massless and there is no slip between pulley and rope.
The pulley radius is and its mass moment of inertia is . Assume that the mass is vibrating harmonically about its static equilibrium position. The natural frequency of the system is
Correct answer
(B) √((kr²)/(J + mr²))
Solution
Let be the displacement of the mass . The rotation of the pulley is . The kinetic energy of the system is . The potential energy of the system is . Using the energy method, . The natural frequency is .
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