Please do it in matlab

3. Design Problem (open-ended problem) The design objective may be to determine the values of the spring constant and/or damping coefficient in order for the response (displacement) or total energy to dissipate to a certain level of its initial value the fastest (within a constraint). How quickly should the response or energy be dissipated in order to achieve optimal designs for passenger comfort? Assume motion starts from rest, vo0. Unless otherwise stated, the nominal values of the mass and the spring stiffness used in all numerical simulations are: m 1,000 kg, k 81,000 N/m. a) System response and energy: (ME 4410 Lab #1 pre-lab) Consider a disturbance Xo applied to the system initially at rest. Plot the response (normalized to xo) of the system for three values of the damping coefficient,c3,000, 18,000, and 25,000 N s/m on a single graph. Properly label your graph with axis labels, title, legend, etc. Obtain a similar plot for the mechanical energy (normalized to the initial energy). What can you learn from the plots? Note that the mechanical energy of the system is: E- + mi2 potential energy stored in the spring kinetic energy of the mass b) Understanding the dissipation time characteristics: Report from the literature on what you understand about the factors that are important to vehicle suspension design for passenger comfort. Provide examples of under-damped and over-damped systems in daily life. Define: i) t as the time instant when the response of the mass is first dissipated to a specified level of the initial displacement (for this project, it is set at 5%). ii) te as the time instant when the total mechanical energy of the system is dissipated to a specified level of the initial energy (for this project, it is set at 5%). ii) Xm as the minimum of the normalized response (the most negative value in Figure 2). You may obtain result by using the built-in function fminsearch (see homework). Note that the displacement could reach 5% of the initial value at more than one instant (see Fig. 2). Obtain graphs of tr,te and xm as functions of c from 2,000 to 30,000 N-s/m. What can you conclude from the results of parts (a) and (b) regarding designs of suspension systems to minimize the vibration or maximize the rate of energy dissipation? What kind of design strategies should be employed? The graphical results in parts (a) and (b)will provide important guidelines for search of optimal solutions using root finding methods. Design optimization: From part (b), you should notice that, for the fixed value of k, there is a minimum value of te for the range of c values. You can then determine the specific value of c that corresponds to this minimum using the MATLAB function min (we have used max before). Now consider a different value of k, the value of c that corresponds to a minimum of te would be different. In this way, with the mass m fixed at 1,000 kg, we can determine and plot the pairs of values of (c,k) that would give minimum te. Compare this curve to the curve of critical damping values in the damping-stifness design space (this forms the basis of a two-parameter design optimization problem). What can you conclude from your results? c) d) Design: With the mass fixed at 1,000 kg, determine the combination of ranges of values of k and c such that lxml