GATE 2016 ME (ME2) – Question 47
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 r and mass 20 kg. The spring constant k is 1500 N/m. If there is no slipping of the rope over the pulley, the natural frequency of the system is_____________ rad/s.
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Correct answer: 9.9 to 10.1
Explanation
Let block displacement be x; the spring changes length by the same magnitude and pulley angular speed is x-prime/r. Assuming a uniform solid-disc pulley, I=Mr²/2=10r², so effective translating mass is5+I/r²=15kg. Natural frequency is sqrt(1500/15)=**10rad/s**. Gravity shifts the equilibrium but does not change linearised stiffness.