dn m, Jo kn WWW kim WWWW Figure 2: Simplified model for the plunge and pitch motions of an aircraft on the ground. Figure 2 shows a simplified model for the plunge (vertical translation) and pitch motions of an aircraft on the ground. The aircraft is modeled as a rigid body of mass m and moment of inertia Jo about the center of mass C. while the nose and main landing gears are modeled as two springs with stiffness constants k,, and km, respectively. The motion is described using the vertical translation he(f) of the center of mass C and the pitch angle o() as the generalized coordinates. The vertical translation and pitch angle are assumed to be positive in the upward and counterclockwise directions, respectively. Following the chosen convention, answer the following questions: 1. Draw the free-body diagram of the system showing magnitude and orientation of any forces and moments 2. Using the Newtonian approach, derive the equations describing the system's motion in the form MII Miz Jhe()) [Kn K12 Jhe(t)) M12 Maz] K12 K22] (4) 8 (1 ) M 40 K 40 showing the expressions of all terms in the mass and stiffness matrices 3. Identify a new pair of generalized coordinates yielding elastic decoupling (but not inertial decoupling) 4. Derive the transformation matrix T relating he() and e() to the new coordinates 5. Using the transformation matrix from Question 4, rewrite Eq. (4) in terms of the new coordinates 6. Using the new coordinates (a) Write the kinetic energy of the system (b) Write the potential energy of the system (c) Verify the system of equations from Question 5 using the Lagrangian approach