We study high-speed friction on soft polymer materials by measuring the amplitude dependence of cyclic lateral forces on the atomic force microscope (AFM) tip as it slides on the surface with fixed contact force. The resulting dynamic force quadrature curves separate the elastic and viscous contributions to the lateral force, revealing a transition from stick-slip to free-sliding motion as the velocity increases. We explain force quadratures and describe how they are measured, and we show results for a variety of soft materials. The results differ substantially from the measurements on hard materials, showing hysteresis in the force quadrature curves that we attribute to the finite relaxation time of viscoelastic surface deformation.