MIT 18 03 - Hour Exam III Solutions (2 pages)

Previewing page 1 of 2 page document View the full content.
View Full Document

Hour Exam III Solutions



Previewing page 1 of actual document.

View the full content.
View Full Document
View Full Document

Hour Exam III Solutions

74 views

Problems/Exams


Pages:
2
School:
Massachusetts Institute of Technology
Course:
18 03 - Differential Equations
Differential Equations Documents

Unformatted text preview:

18 03 Hour Exam III Solutions April 23 2010 1 a The miminal period is 2 b f t is even 1 cos t cos 2 t cos 3 t c xp t 2 2 2 2 2 n 2 n 4 n 4 8 n2 9 2 d There is no periodic solution when n 0 2 3 or 2 a or b 1 1 1 1 c f t u t 1 u t 1 t 1 t 1 fr t u t 1 u t 1 fs t t 1 t 1 t t 3 a v t w t u t w t u d e t e 3 t d 0 0 3 t 3t e 1 e 2 e 3t t t 1 e t e t e 0 e 3t e 3 0 3 3 3 1 1 b W s L w t s 1 s 3 s 3 s 1 2 c W s 2 so p s 12 s2 4s 3 s 1 s 3 s 4s 3 s 1 1 e s s 1 1 t u t so t 1 u t 1 s s s s 10 a b s 1 c b F s 3 By coverup a 10 1 By complex 10 2 2 s 2s 10s s s 1 9 coverup multiply through by s 1 2 9 and set s to be a root say 1 3i b 3i c 1 s 1 9 3i 3i so b 1 c 0 and F s which is the Laplace 1 3i s s 1 2 9 transform of 1 e t cos 3t 4 a 5 a 0 1 3i 1 3i 2 so X s b X s W s F s F s 2 s 4 s 10 3 s 2s2 10s 2 s2 4 MIT OpenCourseWare http ocw mit edu 18 03 Differential Equations Spring 2010 For information about citing these materials or our Terms of Use visit http ocw mit edu terms



View Full Document

Access the best Study Guides, Lecture Notes and Practice Exams

Loading Unlocking...
Login

Join to view Hour Exam III Solutions and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Hour Exam III Solutions and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?