A graphical procedure for constructing the time response of a system from its phase-plane trajectory is described. From this, a graphical solution of the equation x¨ + θ(x˙)g(x) + φ(x˙) + h(x) = F(t) is presented. The construction procedure for the equation x¨ + φ(x˙) + c(t)X(x) = F(t) is detailed as a special case of the more general form
which can also be solved in a similar fashion. The extension of these techniques to higher-order systems is presented.
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