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Consider the rotating disk with an offset slot, as shown in Figure 9.28. Inside the slot is a particle P of mass m connected to a spring with spring constant k. The disk has mass M and moment of inertia I about the center axis (not including the small mass m). The disk is free to rotate about its axis by an angle θ. You can assume that the unstretched length of the spring is zero and at t = 0 the spring is stretched by an amount x0

a. Show that the equations of motion for the mass in the slot and the angle θ of the disk are

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