[10 marks] Consider a second-order system whose response to a unit step input has 20% overshoot, an approximate 2% settling time of 5 seconds, and final (steady-state) value of 4. (a) [4 marks] Find the transfer function for this system, G(s). (b) [1 mark] Use the Laplace Transform Pairs table to write down the step response y(t). (c) [5 marks] Write a MATLAB script to do the following: Compute & and w, precisely. Print them to the Command Window to 6 decimal places. Define a vector of time points from 0 to 20 seconds, spaced 1 millisecond apart. Evaluate the step response y(t) at each of these 20001 time points using the expression from part (b) and your precise calculations of and wr. Calculate the percent overshoot directly from the y(t) data you generated above. Calculate the precise settling time by finding the last point in y(t) that falls outside +2% of the final value. There are several possible approaches. An algorithmic strategy is to examine each point in the step response from beginning to end and update a "bookkeeping" variable if y(tk) > 1.02yfinal or y(tk) < 0.98yfinal at time point tk. When the algorithm terminates, this bookkeeping variable will hold the settling time. Print percent overshoot and settling time to the Command Window to 6 decimal places. Compare your calculations of percent overshoot and settling time to the expected values of 20% and 5 seconds, respectively. Briefly explain any discrepancies. Submit a printout of your code and a screenshot of the output in the Command Window.