ME6443, Test 2
Fall 2007, Dr. Ferri
Name_Solution_
Instructions:
This exam is closed-book and closed-notes; no calculators are allowed. You are allowed to
refer to two 8.5x11-inch or A4-size formula sheets which must be handwritten. Please show
your work.
ME6443, Fall 2007, Dr. Ferri
Homework Solution 2
Due Tuesday, Sept 11, 2007
We wish to find the function y(x) that passes through the points (1,0) and (2,1) and which
minimizes the integral:
I =
2
1
cfw_ x 2 ( y ) 2 + 2 y 2 dx
Problem 1. (2 points)
Show t
ME6443, Fall 2007, Dr. Ferri
Homework Solution 3
Problem 1.
1
Uniform Production Rate
c 1 = 0.3
0.8
c 1 = 0.5
x
0.6
0.4
0.2
0
0
0.1
0.2
0.3
0.4
0.5
Time
0.6
0.7
0.8
0.9
1
Note that, as the relative weighting on the production rate decreases, the productio
ME6443, Fall 2007, Dr. Ferri
Homework Solution 4
Problem 2.
The problem of a string having tension T and length L loaded with a uniform force per unit
length p is given by the following variational statement.
Of all curves y(x) having y(0) = 0, the one th
ME6443, Fall 2007, Dr. Ferri
Homework Solution 8
Due Tuesday, November 27
Problem 1.
A uniform beam of cross-sectional area A, cross-sectional area moment I, length L, density , and
elastic modulus E is shown below. At x = 0, the beam is completely fixed
ME6443, Fall 2007, Dr. Ferri
Homework Solution 9
Due Thursday, December 6
Problem 1.
The strong formulation of a particular problem can be written:
u xu = 1
u ( 0) = 0
u (3) = 0
(1.1)
(1.2)
(1.3)
where ( ) d / dx .
Calculate the approximate solution using
ME6443, Formula Sheet
General:
For the integral I =
x2
x
f (x, y, y' )dx , the extremizing function y(x) satisfies the following Euler-
1
Lagrange equation:
f
d f
=0
y dx y'
f
f
= 0, the Euler-Lagrange equation reduces to:
= C1
y
y'
f
f
If
f = C1
= 0,
mamas. Test 2 Name 50hr. 4m;- it
Instructions:
This exam is closedbook and closednotes. You can not use a calculator. You are allowed to
refer to two, twosided 8.5: | inch or Ital-sized formula sheets. These Fonnula sheets must be
handwritten, and Eou m
ME6443, Test 1, Dr. Ferri
Fall 2007
Name_Solution_
Instructions:
This exam is closed-book and closed-notes. You can not use a calculator. You are allowed to
refer to one, two-sided 8.5x11 inch or A4-sized formula sheet. This formula sheets must be
handwri
ME6443, Fall 2007, Dr. Ferri
Homework Solution 1
Due Thurssday, August 30, 2007
Problem 1. (2 pts)
Find the point (x1, x2, x3) at which the following function attains an extremum. Also, classify the
nature of the extremum (minimum, maximum, saddle.)
2
2
2