Suppose you have a spring attached to a mass at one end and held at the other. the held position is x and the mass position is y as shown in Figure 1. J l) i H ll ',9.' O H l 'l t i ii\" ill. '0 aga l i Position it It (l i O to Figure 1. Spring system attached to a mass at one end and held (manipulated) at the other end. The mass position is y\") and the position of the manipulated end is m). In response to a unit step change in x', y' undergoes a dampened oscillation process as shown in the gure below. 2. 18- 16' El 5 10 15 2D 25 30 3f: 40 time Answer the following questions regarding this system. a. Is this system more appropriately modeled with a first or second order transfer function? Briefly explain. b. Which of the following plots (1-6) best represents the pole(s) (shown in black dots) of the transfer function for this system? Explain. Imaginary Imaginary Imaginary Part 2 Part Part W Real Part Real Part Real Part Imaginary 4 Imaginary Imaginary Part Part Part 4 5 6 Real Part Real Part Real Part c. What is the steady-state Gain of the system