  We describe and implement a technique for extracting forces from the
relaxation of an overdamped thermal system with normal modes. At sufficiently
short time intervals, the evolution of a normal mode is well described by a
one-dimensional Smoluchowski equation with constant drift velocity, v, and
diffusion coefficient, D. By virtue of fluctuation-dissipation, these transport
coefficients are simply related to conservative forces, F, acting on the normal
mode: F = k_BT v/D. This relationship implicitly accounts for hydrodynamic
interactions, requires no mechanical calibration, makes no assumptions about
the form of conservative forces, and requires no prior knowledge of material
properties. We apply this method to measure the electrostatic interactions of
polymer microspheres suspended in nonpolar microemulsions.
