3. The figure below shows a simplified model of a rate gyroscope, which is an instrument that can be mounted in a vehicle to determine the vehicle's angular velocity about a specific axis in this case "yaw" angular velocity about a vertical axis. Assume that the gyroscope rotor spin rate o and vehicle's yaw angular velocity o are constant. A linear spring and torsional damper restrict the motion of so that it can be measured. (Whenever o 0, the rotor pitch angle will also be nonzero.) Derive the equation of motion for 0, and show that when o≫o, the steady-state value of is proportional to o Yaw velocity Pitch damper, b

3. The figure below shows a simplified model of a rate gyroscope, which is an instrument that can be mounted in a vehicle to determine the vehicle's angular velocity about a specific axis in this case "yaw" angular velocity about a vertical axis. Assume that the gyroscope rotor spin rate o and vehicle's yaw angular velocity o are constant. A linear spring and torsional damper restrict the motion of so that it can be measured. (Whenever o 0, the rotor pitch angle will also be nonzero.) Derive the equation of motion for 0, and show that when o≫o, the steady-state value of is proportional to o Yaw velocity Pitch damper, b