ME 3220 Fall 2020 PROJECT Due: Thursday, December 3, 2020 You must solve both problems described below to receive full points. Important Note: The project counts for 20% of the final grade. First Problem (50 Points) A one degree-of-freedom model of a motor vehicle travelling in the horizontal direction is shown in Figure 2.17 (Inman, 4th edition) and class notes. (i) Find analytically the relative vertical displacement of the vehicle as it travels over a wavy road of the form y(s) Y sin(πs / δ) , where Y is the amplitude of the wave form, s is the travelled distance, and 10Y . (ii) Write a MATLAB program for finding the relative vertical displacement of the vehicle as it travels over a road bump of the form y(s) Y sin(πs / δ) and compare the numerical solution to the analytical solution. (25 points) (iii) Use the computer program to find numerically and plot the relative vertical displacement when the vehicle travels over the double step shown below. (25 points) Parameter values: k = 400 kN/m, m = 1200 kg, ζ = 0.5, Y = 0.3 m, δ = 6 m. Attention: If you answer only question (i), the problem will NOT be graded and it will count for NOTHING. Important Note: You need to send me a report and a working MATLAB code that runs from one starting “run” point ME 3220 Fall 2020 Second problem (50 points) Write a MATLAB program that can compute the response of an underdamped spring- mass system for an arbitrary periodic input. 1. Show that your program can derive the analytical solution for a mass-spring system governed by the equation mx cx Kx F t , with 1m kg , 10c kg s , 100K N m , and F t is the square-pulse function with amplitude 0 10F N and period 2 secondsT . We assume that the initial conditions are 0 0.1x m and 0 3x m s . (Note: It is the example that we solved in class). 2. Show that your program can derive the solution for any arbitrary periodic force with two examples. Important Note: You need to send me a report and a working MATLAB code that runs from one starting “run” point
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