1. Figure 1 shows a spring-mass-damper system with a force actuator for position. control. The linear spring has stiffness k, the linear damper has coefficient c, the block has mass m, and the position of the mass is x. m =1 slug, c = 12 (lb-s/ft), and k = 49 (lb/ft). Actuator m → Figure 1 a. (15 points) Assuming all initial conditions are zero, what is the open loop transfer function of the spring-mass-damper system with the actuating force F as input and the position x as output? b. (10 points) Find the natural frequency and damping ratio of this system. c. (5 points) This is a (under, critically, over) damped system.