Rate and state frictional parameters are typically determined using two types of experimental protocols: velocity steps and slide-hold-slide events. Here we take a new approach by examining the frictional response to controlled, harmonic oscillations in load point velocity. We present a Matlab graphical user interface software package, called RSFitOSC, that allows users to easily determine frictional parameters by fitting oscillation events using the rate and state friction equations. We apply our new methods to a set of ice-rock friction experiments conducted over a temperature range of -16.4°C to -2°C, and described in a companion paper: McCarthy et al. (In Review). Values of the frictional stability parameter (a-b) determined from oscillations reveal dominantly velocity-weakening behavior across the entire range of experimental conditions. However, values of (a-b) determined from velocity steps in the same experiments yield velocity-strengthening behavior. We also show that the elastic stiffness of the ice-rock system depends on the temperature, and is unlikely to be explained by changes in the elastic properties of ice. Load point velocity oscillations induce oscillations in applied shear stress. Many natural fault systems exhibit slip behaviors that depend on harmonic oscillations in applied tidal stresses. Our new method provides a way to study how frictional properties directly depend on parameters relevant to tidal forcing, and how oscillatory loading must be considered when extracting friction parameters.