An airplane standing on a runway Is shown In Fig. The airplane has a mass m = 20,000 kg and a mass moment of inertia J0 = 50 x 106 kg-m2. If the values of stiffness and damping constant are =10 kN/m and c2 = 2 RN-Wm for the main landing gear and k2 = 5 kN/m and c2 = 5KN-s/m for the nose landing gear, (a) derive the equations of motion of the airplane, and (b) find the undamped natural frequencies of the system. Assume /1 = 20 m and 12 = 30 m.

Figure:

Main landing gear m.Je + Nose landing gear