Lecture 1

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Unformatted text preview: . This is an example of a boundary value problem (BVP) for a fourth-order linear ODE. This is a boundary value problem because: Observe that y(t) = 0 is a solution of this problem for all values of and l. A more interesting problem is to determine y and those values of and l for which non-trivial (y(t) 6= 0) solutions exist. As such, this BVP is also a di erential eigenvalue problem. Nontrivial solutions y(t) are called eigen functions and their corresponding values of are eigenvalues. y(t) P P t Figure 1.1.2: Buckling of an elastic column. 4. Pendelum Oscillations ( 1], Section 1.3). The position (x(t) y(t)) at time t of a particle of mass m oscillating on a pendelum of length l (Figure 1.1.3) is 2 m d x = ;T sin = ; T x dt2 l m d y = mg ; T cos = mg ; T y dt2 l 2 t>0 where g is the acceleration of gravity, T (t) is the tension in the string, and (t) is the angle of the pendelum relative to the vertical at time t (Figure 1.1.3). These equations are, however, insu cient to guarantee that the particle stays on the string. T...
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This document was uploaded on 03/16/2014 for the course CSCI 6820 at Rensselaer Polytechnic Institute.

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