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GATE2019-1-43

A uniform thin disk of mass $1 \: kg$ and radius $0.1 \: m$ is kept on a surface as shown in the figure. A spring of stiffness $k_1=400 \: N/m$ is connected to the disk center $A$ and another spring of stiffness $k_2=100 \: N/m$ is connected at point $B$ just above the point $A$ 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 _____ $rad/s$ (round off to oe decimal place).

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