Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
The behaviour of an unforced mechanical system is governed by the differential equation 5 2 -1 0 x(t) = 3 6 -9 x(t), x(0) = 1 1 0 (a) Show that the eigenvalues of the system matrix are 6, 3, 3 and that there is only one linearly independent eigenvector corresponding to the eigenvalue 3. Obtain the eigenvectors corresponding to the eigenvalues 6 and 3 and a further generalized eigenvector for the eigenvalue 3. (b) Write down a generalized modal matrix M and confirm that AM = MJ for an appropriate Jordan matrix J. x(t) = MeM-¹x(0) obtain the solution to the given differential equation. (c) Using the result

The behaviour of an unforced mechanical system is governed by the differential equation 5 2 -1 0 x(t) = 3 6 -9 x(t), x(0) = 1 1 0 (a) Show that the eigenvalues of the system matrix are 6, 3, 3 and that there is only one linearly independent eigenvector corresponding to the eigenvalue 3. Obtain the eigenvectors corresponding to the eigenvalues 6 and 3 and a further generalized eigenvector for the eigenvalue 3. (b) Write down a generalized modal matrix M and confirm that AM = MJ for an appropriate Jordan matrix J. x(t) = MeM-¹x(0) obtain the solution to the given differential equation. (c) Using the result

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 18EQ
See similar textbooks
icon
Related questions
Question
The behaviour of an unforced mechanical system is governed by the differential equation 5 2 -1 0 x(1) = 3 6-9 x(t), x(0) = 1 1 1 1 0 (a) Show that the eigenvalues of the system matrix are 6, 3, 3 and that there is only one linearly independent eigenvector corresponding to the eigenvalue 3. Obtain the eigenvectors corresponding to the eigenvalues 6 and 3 and a further generalized eigenvector for the eigenvalue 3. (b) Write down a generalized modal matrix M and confirm that AM = MJ for an appropriate Jordan matrix J. x(t) = Me M-¹x(0) obtain the solution to the given differential equation. (c) Using the result
Transcribed Image Text:The behaviour of an unforced mechanical system is governed by the differential equation 5 2 -1 0 x(1) = 3 6-9 x(t), x(0) = 1 1 1 1 0 (a) Show that the eigenvalues of the system matrix are 6, 3, 3 and that there is only one linearly independent eigenvector corresponding to the eigenvalue 3. Obtain the eigenvectors corresponding to the eigenvalues 6 and 3 and a further generalized eigenvector for the eigenvalue 3. (b) Write down a generalized modal matrix M and confirm that AM = MJ for an appropriate Jordan matrix J. x(t) = Me M-¹x(0) obtain the solution to the given differential equation. (c) Using the result
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
SEE MORE TEXTBOOKS