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A uniform thin disk of mass 1 kg and radius 0.1 m is kept on a surface as shown in the figure. The spring of stiffness k1 = 400 N/m is connected to the disk center A and another spring of stiffness k2 = 100 N/m is connected at point B just above point A on the circumference of the disk. Initially, both the springs are unstretched. A 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 one decimal place).
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- 23.1 rad / sec
- 123.1 rad / sec
- 213.1 rad / sec
- 231.1 rad / sec
Correct Option: A
Given, Disc mass m = 1 kg, R = 0.1 m
K1 = 400 N/m, K2 = 100 N/m
By assuming pure rolling of the disc, Mc = 0 at I.C. at point (C)
Icθ̇̇ + K2(2R)θ × 2R + K1Rθ × R = 0
| Ic = Idisc + mR2 = | + mR2 | |
| 2 |
| = | mR2 = | × 0.12 = 1.5 × 10-2 | ||
| 2 | 2 |
⇒ ωn = √533.3rad / sec
ωn = 23.094 rad / sec
ωn = 23.1 rad / sec
