Problem 2: MATLAB can determine the zero-state response for an arbitrary input given th ODE description of the system. For example, suppose we want to determine the unit-step respons of a second-order system described by the ODE y + 4y + 100y = 200f(t) using MATLAB. The first step is to represent the ODE as Q(D)y(t) = P(D)f(t) where Q(D) = D2 + 4D + 100 P(D) = 200. In MATLAB these polynomials are represented as >> Q = [1, 4, 100); >> P = [200]; The MATLAB command >> step (P,Q) generates a plot of the unit-step response over a time interval determined by MATLAB. To generat the unit-step response at 200 points over a specified time interval, say 0 > Q = [1, 4, 100); >> P = [200]; >> t = linspace(0, 5, 200); >> step(P,Q, t) You can also save the response to a vector y using You can also save the response to a vector y using >> Q = [1, 4, 100); >> P = [200]; t = linspace(0, 5, 200); >> y = step(P,Q, t); ^ ^ You can also find the zero-state response for an arbitrary input f(t) using the MATLAB command Isim. For example, to find the zero-state response of our second-order system for the input f(t) = e-tu(t) at 100 points over the interval 0 > Q = [1, 4, 100); >> P = [200]; >> t = linspace(0, 4); >> f = exp(-t); >> lsim(P,Q, f, t); The last MATLAB command automatically generates a plot. You can also save the response to a vector y by replacing the last line with >> y = lsim(P,Q, f, t); Using the MATLAB command lsim, write a MATLAB m-file that plots the unit-step response of the second order system haswam op uwaule) = Kw]f() for three different sets of parameters Wn = 10rad/ sec, 5 = 0.2, K = 2 Wn = 10rad/sec, 5 = 1.0, K = 2 wn = 10rad/ sec, 5 = 2.0, K = 2 in a single figure. Use the legend to distinguish the plots by the value of $ (you can generate the character 5 by using \zeta). Based on your plots, what is the physical significance of the parameter K? Use the gtext command to add your name and section number to the figure. You must turn in the figure along with the m-file to receive credit