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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
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 . ______________________________________...
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- Spring '08