Mechanical Engineering homework help

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 springmass 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
m kg 1 , c kg s 10 ,
K N m 100
, and
F t 
is the square-pulse function with amplitude
0 F N 10
and
period
T  2 seconds 
. We assume that the initial conditions are
x m 0 0.1  
and
x m s 0 3  
. (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