  Using an expansion in order parameters, the equation of motion for the
centroid of globally coupled oscillators with natural frequencies taken from a
distribution is obtained for the case of high coupling, low dispersion of
natural frequencies and any number of oscillators. To the first order, the
system can be approximated by a set of four equations, where the centroid is
coupled with a second macroscopic variable, which describes the dynamics of the
oscillators around their average. This gives rise to collective effects that
suggest experiments aimed at measuring the parameters of the population.
