# X2 it now follows from newtons second law of motion

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Unformatted text preview: 1,1},{1,3,2},{1,2,4}}; Eigenvalues[a] The answer is so complicated because Mathematica uses exact but complicated formulae for solving cubics discovered by Cardan and Tartaglia, two sixteenth century Italian mathematicians. b. Find numerical approximations to these eigenvalues by running the program Eigenvalues[N[a]] The numerical values of the eigenvalues are far easier to use. c. Use Mathematica to ﬁnd numerical values for the eigenvectors for A by running the Mathematica program Eigenvectors[N[a]] and write down the general solution to the matrix diﬀerential equation dx = Ax. dt 48 1 Figure 2.5: Two carts connected by springs and moving along a friction-free track. 2.4 Mechanical systems Mechanical systems consisting of weights and springs connected together in an array often lead to initial value problems of the type d2 x = Ax, dt2 x(0) = f , dx = 0, dt (2.13) where A is a symmetric matrix and f is a constant vector. These can be solved by a technique similar to that used in th...
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