The disk rotates in the horizontal plane with constant angular velocity Ω = 12 rad/s. The...

The disk rotates in the horizontal plane with constant angular velocity Ω = 12 rad/s. The mass m = 2 kg slides in a smooth slot in the disk and is attached to a spring with constant k = 860 N/m The radial position of the mass when the spring is unstretched is r = 0.2 m.

(a) Determine the “equilibrium” position of the mass, the value of r at which it will remain stationary relative to the center of the disk.

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(b) What is the frequency of vibration of the mass relative to its equilibrium position?

Strategy: Apply Newton’s second law to the mass in terms of polar coordinates.