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Unformatted text preview: modify the program by asking for only the smallest eigenvalue lambda[[n]] and a plot of the corresponding eigenvector: n = 14; m = Table[Max[2-Abs[i-j],0], {i,n-1} ,{j,n-1} ]; p = m - 4 IdentityMatrix[n-1]; a = n∧2 p; eval = Eigenvalues[N[a]]; evec = Eigenvectors[N[a]]; Print[eval[[n-1]]]; ListPlot[evec[[n-1]]]; If we experiment with this program using different values for n, we will see that as n gets larger, the smallest eigenvalue seems to approach −π 2 and the plot of the smallest eigenvector looks more and more like a sine curve. Thus the fundamental frequency of the mechanical system seems to approach π/2π = 1/2 and the oscillation in the fundamental mode appears more and more sinusoidal in shape. When n is large, we can consider this array of springs and weights as a model for a string situated along the x-axis and free to stretch to the right and the left along the x-axis. The track on which the cart runs restricts the motion of the weights to be only in the x-direction. A more...
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This document was uploaded on 01/12/2014.

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