In 41 and 42, a mass-spring-dashpot system with external force f(t) is described. Under

Chapter 4, Problem 4.5.41

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In 41 and 42, a mass-spring-dashpot system with external force f(t) is described. Under the assumption that x(O) = x'(O) = 0, use the method of Example 8 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 f(t) = A[2ut -n)(t -2n)(t -3n) . (t -4n)(t -Sn)(t -6n)) - 1] has the value +A if 0 < t < n, the value -A ifn < t < 2n, and so forth, and hence agrees on the interval [0, 6n] with the square-wave function that has amplitude A and period 2n. (See also the definition of a square-wave function in terms of sawtooth and triangular-wave functions in the application materialfor this section.) m = 1, k = 4, c = 0; f(t) is a square-wave function with amplitude 4 and period 2n.