A damping device is used to reduce the undesired vibrations of machines. A viscous fluid, such as a heavy oil, is placed between the wheels, as shown in Figure P2.40. When vibration becomes excessive, the relative motion of the two wheels creates damping. When the device is rotating without vibration, there is no relative motion and no damping occurs. Find θ1(s) and θ2(s). Assume that the shaft has a spring constant K and that b is the damping constant of the fluid. The load torque is T.

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Duter wheol Inner wheel Shaft Fluid, b FIGURE P2.40 Cutaway view of damping device.