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Grading Guide
Content
Met
Partially Met
Not Met
Comments:
Calculate the company’s weighted average cost of capital.
Use the dividend discount model.
Shows calculations in Microsoft® Word.
Explain and defend why he/she agrees or disagrees with this
3. statement:
The company’s CEO has stated that if the company increases
the amount of long term debt, so that the capital structure will
be 60% debt and 40% equity, this will lower its WACC.
Reports what he/she would advise the CEO.
The analysis is 700 words in length.
Total Available
Total Earned
5
#/5
Writing Guidelines
Met
Partially Met
Not Met
Comments:
The paper—including tables and graphs, headings, title page,
4. and reference page—is consistent with APA formatting
guidelines and meets course-level requirements.
Intellectual property is recognized with in-text citations and a
reference page.
Paragraph and sentence transitions are present, logical, and
maintain the flow throughout the paper.
Sentences are complete, clear, and concise.
Rules of grammar and usage are followed including spelling and
punctuation.
Total Available
Total Earned
5. 2
#/2
Assignment Total
#
7
#/7
Additional comments:
ENGR 516 Computational Methods for Graduate Students
Catholic University of America
Assignment #6
EigenValue Problems
1.) The moment of inertia, Ix, Iy, and the product of inertia Ixy
of the cross sectional area
shown in the figure are:
2.) The structure of an acetylene molecule may be idealized as
four masses connected by
two springs as shown in the figure below. Applying the
equation of motion; we can
generate a system model for the amplitudes of vibration of each
atom:
1
6. Excerpts from this work may be reproduced by instructors for
distribution on a not-for-profit basis
for testing or instructional purposes only to students enrolled in
courses for which the textbook
has been adopted. Any other reproduction or translation of this
work beyond that permitted by
Sections 107 or 108 of the 1976 United States Copyright Act
without the permission of the
copyright owner is unlawful.
4.23 The moment of inertia , , and the product of inertia of the
cross-sectional area shown in the figure are:
mm4, mm4, and mm4
The principal moments of inertia are the eigenvalues of the
matrix
, and the principal axes are in the direction of the eigen-
vectors. Determine the principal moments of inertia by solving
the char-
acteristic equation. Determine the orientation of the principal
axes of
inertia (unit vectors in the directions of the eigenvectors).
Solution
The eigenvalues of the matrix are the principal moments of
7. inertia. They are determined from
the roots of the characteristic equation:
which simplifies to .
The equation is solved by using the quadratic formula:
or and
By definition, the eigenvectors corresponding to each
eigenvalue must satisfy:
Starting with the first eigenvalue:
These two equations are redundant and yield .
Since the eigenvector is a unit vector: .
4 mm
O
y
8. x
24 mm
2 mm
20 mm
3 mm
2 mm
Ix Iy Ixy
Ix 5286= Iy 4331= Ixy 2914=
5286 2914
2914 4331
5286 2914
2914 4331
5286 λ–( ) 4331 λ–( ) 2914( ) 2914( )– 0=
14402270 9617λ– λ2+ 0=
11. u1
1( ) 1.1772u2
1( )=
u1
1( )( )
2
u2
1( )( )
2
+ 1=
1
Excerpts from this work may be reproduced by instructors for
distribution on a not-for-profit basis
for testing or instructional purposes only to students enrolled in
courses for which the textbook
has been adopted. Any other reproduction or translation of this
work beyond that permitted by
12. Sections 107 or 108 of the 1976 United States Copyright Act
without the permission of the
copyright owner is unlawful.
4.23 The moment of inertia , , and the product of inertia of the
cross-sectional area shown in the figure are:
mm4, mm4, and mm4
The principal moments of inertia are the eigenvalues of the
matrix
, and the principal axes are in the direction of the eigen-
vectors. Determine the principal moments of inertia by solving
the char-
acteristic equation. Determine the orientation of the principal
axes of
inertia (unit vectors in the directions of the eigenvectors).