31 EXERCISES 2 show that the system x = x-sint with x(0) = 1/2 admits the periodic solution x(t) = (1/2) (sint + cost). How does this reconcile with our claim that id autonomous systems do not admit periodic solutions? ③ Likewise show that the system X = - w ² x with x (0) = 0 admits the periodic solution x(t) = sin (wt). Again, how do we reconcile this paradox?
31 EXERCISES 2 show that the system x = x-sint with x(0) = 1/2 admits the periodic solution x(t) = (1/2) (sint + cost). How does this reconcile with our claim that id autonomous systems do not admit periodic solutions? ③ Likewise show that the system X = - w ² x with x (0) = 0 admits the periodic solution x(t) = sin (wt). Again, how do we reconcile this paradox?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:31
EXERCISES
2 show that the system x = x-sint with
x(0) = 1/2 admits the periodic solution
x(t) = (1/2) (sint + cost). How does this
reconcile with our claim that id autonomous
systems do not admit periodic solutions?
③ Likewise show that the system X = - w ² x
with x (0) = 0 admits the periodic solution
x(t) =
sin (wt). Again, how do we reconcile
this paradox?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 6 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
