【Abstract】In this paper the author has made a complete topological analysis on a machine oscillation problem governed by a third order nonlinear differential equation of the following form: A(d3δ)/(dt3)+(d2δ)/(dt2)-Acotδ(dδ)/(dt)(d2δ)/(dt2)+((PiA)/M)cotδ+Csin2δ)(dδ)/(dt)+Bsinδ-(Pi)/M=0 and has suggested a simple graphical method for the system performance computation. A numerical example is given for illustration.