In Problem 21.53, the radius R = 250 mm, k = 150 N/m, and the moment of inertia of the dis...

In Problem 21.53, the radius R = 250 mm, k = 150 N/m, and the moment of inertia of the disk is I = 2 kg-m2.

(a) At what value of c will the system be critically damped?

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(b) At t = 0. the spring is unstretched and the clockwise angular velocity of the disk is 10 rad/s. Determine θ as a function of time if the system is critically damped.

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(c) Using the result of (b), determine the maximum resulting angular displacement of the disk and the time at which it occurs.

(See Example 21.4.)