b1 sin b2 sin 2 t t t t 31 in this

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Unformatted text preview: realistic model would allow the carts to move in all three directions. This would require new variables yi and zi such that yi (t) = the y -component of displacement of the i-th weight, zi (t) = the z -component of displacement of the i-th weight. 60 20 40 60 80 100 -0.02 -0.04 -0.06 -0.08 -0.1 -0.12 -0.14 Figure 2.9: Shape of the fundamental mode (n=100). If we were to set x1 x x = 2 , · xn x1 x y = 2 , · xn z1 z z = 2 , · zn then an argument similar to the one given above would show that the vectors x, y and z would satisfy the matrix diﬀerential equations dx k = Ax, dt m dy k = Ay, dt m dz k = Az. dt m and each of these could be solved just as before. Using a similar approach, we could consider even more complicated systems consisting of many masses and springs connected in a two- or three-dimensional array. 61 Chapter 3 Fourier Series 3.1 Fourier series The theory of Fourier series and the Fourier transform is concerned with dividing a function into a superposition of sines and cosines, its components of various frequenci...
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This document was uploaded on 01/12/2014.

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