In Problems 36 and 37, a massspringdashpot system with external force f (t) is described. Under the

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In Problems 36 and 37, a mass–spring–dashpot system with external force f (t) is described. Under the assumption that x(0) = x'(0) = 0, use the method of Example 7 to find the transient and steady periodic motions of the mass. Then construct the graph of the position function x(t). If you would like to check your graph using a numerical DE solver, it may be useful to note that the function

has the value + A if 0 < t < π, the value -A if π < t < 2π, and so forth, and hence agrees on the interval [0,6π] with the square wave function that has amplitude A and period 2π. (See also the definition of a square wave function in terms of sawtooth and triangular wave functions in the application material for this section.)

m = 1, k = 10, c = 2; f(t) is a square wave function with amplitude 10 and period 2π.

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Differential Equations And Linear Algebra

ISBN: 9780134497181

4th Edition

Authors: C. Edwards, David Penney, David Calvis

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