A solution is given for the problem of finding a transition or switching curve in the phase plane for the expression mx + cx + kx = Df(x,x) so that solutions reach the zero state in a minimum time. The solution has applications in the design of servomechanisms and similar systems; f is a discontinuous function which assumes only + of - 1. The solution required the problem to be broken up into cases. Curves are included showing points in the xx phase plane at which f switches from +1 to -1 and vice versa.