The rotor of an electric generator weighs m = 200 kg and is attached to a...

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The rotor of an electric generator weighs m = 200 kg and is attached to a platform weighing M = 1000 kg as shown in Figure 2. The rotor has an eccentricity of a. The equivalent stiffness of the spring connecting the platform to ground is k = 8.5 x 106N/m, and the equivalent damping connection of the platform to ground is c = 14 kN s/m. The maximum operating speed of the generator is 1000 rpm. The rotor will run at a certain constant operating speed. Neglect the friction between the platform and ground and only consider the motion in horizontal direction. Rotor www Platform k Figure 2: Rotor and platform assembly. (a) Set up proper coordinate system. Derive the EOM of this system using symbolic variables. (b) Find the value of natural frequency w, damped frequency wa, damping coefficient (c) Steady-state vibration amplitude using symbolic variables. (d) Determine the allowable amount of eccentricity a so that the steady-state amplitude does not exceed 0.25 mm at an operating speed of 600 rpm. (e) If a = 0.2 mm, determine the allowable range of operating speed of the rotor so that the system's the steady-state amplitude does not exceed 0.2 mm. The rotor of an electric generator weighs m = 200 kg and is attached to a platform weighing M = 1000 kg as shown in Figure 2. The rotor has an eccentricity of a. The equivalent stiffness of the spring connecting the platform to ground is k = 8.5 x 106N/m, and the equivalent damping connection of the platform to ground is c = 14 kN s/m. The maximum operating speed of the generator is 1000 rpm. The rotor will run at a certain constant operating speed. Neglect the friction between the platform and ground and only consider the motion in horizontal direction. Rotor www Platform k Figure 2: Rotor and platform assembly. (a) Set up proper coordinate system. Derive the EOM of this system using symbolic variables. (b) Find the value of natural frequency w, damped frequency wa, damping coefficient (c) Steady-state vibration amplitude using symbolic variables. (d) Determine the allowable amount of eccentricity a so that the steady-state amplitude does not exceed 0.25 mm at an operating speed of 600 rpm. (e) If a = 0.2 mm, determine the allowable range of operating speed of the rotor so that the system's the steady-state amplitude does not exceed 0.2 mm.