A rotor is mounted in bearings that are free to move in a single plane, as shown in the following figure. The rotor has total mass M and moment inertia JG (JG=ML) about its center of gravity. a. Draw free body diagram of the system. b. Derive the equation of motion. c. For L = 0.75 L and L = 0.25 L, calculate natural frequencies of the system. d. For L= 0.75 L and L = 0.25 L, calculate mode shapes of the system. Find and sketch node location for each mode shape. 414 414 ww 4 4