Problem 1. Figure 1 shows homogeneous cylinder of diameter D and mass M that is free to rotate about its rotational axis and that is connected to the wall through a series of 2 springs. The cylinder has translational motion away from the wall. Assume that the displacement and angular displacement of the cylinder are measured from equilibrium positions. M k1 k2 wwww Figure 1. Simplified diagram of homogeneous cylinder with springs rolling. 1. 2 pts - Identify and show all variables/coordinates. 2. 5 pts - State all assumptions and cite references as appropriate. 3.3 pts - What is the Kinetic Energy of the system? 4.2 pts - What is the Potential Energy of the system? 5.5 pts - Derive the equations of motion of the system in terms of position only. 6.3 pts - What is the natural frequency of the system?