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Wright State University Spring 2016
Department of Mechanical and Materials Engineering
ME 1020: ENGINEERING PROGRAMMING WITH MATLAB
FINAL EXAM
Open Book, Closed Notes, Do Not Write on this Sheet
Create a Separate MATLAB Script File for Each Problem
Submit all MATLAB files (.m) to Dr. Thomas
Each MATLAB File Must Have the Following Header:
Problem 1 ( 4 Points): Create a MATLAB script file to calculate and plot the derivative of the function ๐ฆ
โ๐ฅ
sin( 3 ๐ฅ) from 0 โค ๐ฅ โค 4 using the Forward Difference Method described in class (shown below). You must
use a for loop to solve this problem. Provide a plot title and labels for the axes. Use 101 points from ๐ฅ = 0 to
Problem 2 ( 4 Points): Create a MATLAB script file to calculate and plot the integral of the function ๐ฆ
โ๐ฅ
sin( 3 ๐ฅ) from 0 โค ๐ฅ โค 4 using the Trapezoidal Method described in class (shown below). You must use a
for loop to solve this problem. Provide a plot title and labels for the axes. Use 101 points from ๐ฅ = 0 to ๐ฅ = 4.
trapezoid
2
1
1
2
Problem 3 ( 4 Points): Create a MATLAB script file that uses the Euler Method discussed in class to solve the
following differential equation. Plot the solution from 0 โค ๐ก โค 0. 2. Provide a plot title and labels for the axes.
You must use a for loop to solve this problem. Show that ๐ฆ
3 / 2
Euler Method: ๐ฆ(๐ก
๐+ 1
๐
) + โ๐ก โ ๐[๐ก
๐
๐
)]
Problem 4 ( 4 Points): Create a MATLAB script file that uses the Euler Method discussed in class to solve the
following differential equation. Plot the solution from 0 โค ๐ก โค 0. 2. Provide a plot title and labels for the axes.
You must use a for loop to solve this problem. Show that ๐ฆ(๐ก = 0. 2 ) = 3. 1359.
3 / 2
Euler Method: ๐ฆ(๐ก
๐+ 1
๐
) + โ๐ก โ ๐[๐ก
๐
๐
)]
Problem 5 ( 4 Points): Create a MATLAB SIMULINK model to solve the following differential equation. Plot
the solution from 0 โค ๐ก โค 0. 2.
3 / 2
% Final Exam, ME 1020, Spring 2016, Your Name Here
% Problem 2
clc, clear all, close all
N = 101;
x = linspace(0,4,N);
y = exp(-x).sin(3x);
inty(1) = 0;
for k = 1:N- 1
inty(k+1) = inty(k) + 0.5(x(k+1)-x(k))(y(k)+y(k+1));
end
plot(x,y,x,inty)
xlabel('x'),ylabel('y(x) and int y(x)')
title('Problem 2: Scott Thomas')
legend('y(x)','int y(x)','Location','Best')
Published with MATLABยฎ R2012b
% Final Exam, ME 1020, Spring 2016, Your Name Here
% Problem 3
clc, clear all, close all
N = 500000
tfinal = 0.2;
deltat = tfinal/(N-1);
y(1) = 3;
t(1) = 0;
for k = 1:N- 1
y(k+1) = y(k) + deltat*((y(k))^(3/2) + 2);
t(k+1) = t(k) + deltat;
end
t(N)
y(N)
plot(t,y)
xlabel('t'),ylabel('y(t)')
title('Problem 3: Scott Thomas')
N =
500000
ans =
ans =
% Final Exam, ME 1020, Spring 2016, Your Name Here
% Problem 4
clc, clear all, close all
N = 50000
tfinal = 0.2;
deltat = tfinal/(N-1);
x1(1) = 3;
x2(1) = 0;
t(1) = 0;
for k = 1:N- 1
x1(k+1) = x1(k) + deltat*x2(k);
x2(k+1) = x2(k) + deltat*(-x2(k) + (x1(k))^(3/2) + 2);
t(k+1) = t(k) + deltat;
end
t(N)
x1(N)
plot(t,x1)
xlabel('t'),ylabel('y(t)')
title('Problem 4: Scott Thomas')
N =
50000
ans =
ans =
Published with MATLABยฎ R2012b
