A new method for extracting quantitative data from amplitude modulation dynamic force-distance measurements is developed. The method is based on the harmonic oscillator model of vibrating atomic force microscope cantilevers, and is capable of extracting both the conservative and dissipative parts of the tip-sample interaction from a measurement of oscillation amplitude and phase as a function of distance. Numerical simulations are used to demonstrate the validity of the method. Further proof of the accuracy of this method is provided by a measurement of electrostatic forces between an AFM tip and a graphite sample.