Answer: A mass m on a spring with constant k satisfies the differential equation (see
Chapter 7, Problem 28(choose chapter or problem)
A mass m on a spring with constant k satisfies the differential equation (see Section 3.7) mu + ku = 0, where u(t) is the displacement at time t of the mass from its equilibrium position. (a) Let x1 = u, x2 = u , and show that the resulting system is x = 0 1 k/m 0 x. (b) Find the eigenvalues of the matrix for the system in part (a). (c) Sketch several trajectories of the system. Choose one of your trajectories, and sketch the corresponding graphs of x1 versus t and of x2 versus t. Sketch both graphs on one set of axes. (d) What is the relation between the eigenvalues of the coefficient matrix and the natural frequency of the springmass system?
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