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 𝑘1 = 400 N/m is

Q. 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 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. 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).

Sol:

As per given date
Disc mass,

m = 1 kg
Radius, r = 0.1 m
torque equation about point ‘o’