Problem 1: CAM Dynamics Consider a cam follower system in an ultralight aircraft engine. The system can be simplified by using the following one-dimensional model of a damped cam-follower system from your course reader. 000 me tx ke ts The mass of the system me is 0.5 kg. The spring constant of the system ke is 500 kN/m. a. Find the equation of motion for the figure above. b. Derive the equation for the natural frequency of the system if it is undamped. Show all of your work. c. Solve for the natural frequency of the system in radians per second. d. Solve the equation of motion in part a. for position x(t). Use the characteristic equation shown in the hints. You do not have to solve for arbitrary C and C2 of the characteristic equation shown in the hints or solve for the constants in the figure above. Include damping. Show all your work. Hint: Assume the solution for x in the form of x(t) = Ce + Cze2. e. What additional information do you need in order to solve for arbitrary constants C1 and C2 in the equation you have created in part d.? f. Derive the equation for the critical damping coefficient. Show all of your work. g. Solve for the critical damping coefficient of the system in N's/m. h. Write an equation that relates the critical damping coefficient derived in part f. to the natural frequency of the system.