I a it can be shown that the partial sums on the left

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: hence the functions are linearly independent at every point. 28 . Let and . It follows that and . In terms of the new variables, we obtain the system of two first order ODEs . The associated eigenvalue problem is . The characteristic equation is , with roots . Since the eigenvalues are purely imaginary, the origin is a center. Hence the phase curves are ellipses, with a clockwise flow. For computational purposes, let and . ________________________________________________________________________ page 401 —————————————————————————— CHAPTER 7. —— . The general solution of the second order equation is . The general solution of the system of ODEs is given by ________________________________________________________________________ page 402 —————————————————————————— CHAPTER 7. —— x It is evident that the natural frequency of the system is equal to . ______________________________________...
View Full Document

This note was uploaded on 03/11/2014 for the course MA 303 taught by Professor Staff during the Spring '08 term at Purdue.

Ask a homework question - tutors are online