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.

Transcribed Image Text:

f(t) = A[2u((tл)(1-2л)(t - 3л). (t - 4)(t - 5)(t - 6л)) - 1]