GATE 2019 ME (ME1) – Question 53
A uniform thin disc of mass 1 kg and radius 0.1 m rolls without slipping as shown. Spring k1 = 400 N/m attaches to centre A; spring k2 = 100 N/m attaches to rim point B directly above A. Both are initially unstretched. Find natural frequency of small vibrations (rad/s), to one decimal place.
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Correct answer: 23 to 24
Explanation
Centre displacement $x$ moves the upper attachment by $2x$. Equivalent stiffness is $400+100(2)^2=800$ N/m. Effective mass is $m+I/r^2=1+1/2=1.5$ kg. Hence $\omega_n=\sqrt{800/1.5}=23.094$, or **23.1 rad/s**.