1. A method for characterizing a nonlinear system using the system's steady state response comprising: exciting a transducer using a plurality of frequencies while decoupled from the nonlinear system; wherein the nonlinear system is a sample, wherein the transducer is a cantilever attached to a piezo stack, and the cantilever has a tip attached to the opposite end, wherein the tip interacts with the sample, wherein exciting is performed by function generators coupled to the piezo stack, measuring the amplitude of response of each of the plurality of frequencies while decoupled from the nonlinear system; exciting the transducer using the plurality of frequencies while coupled to the nonlinear system; measuring the amplitude of response of each of the plurality of frequencies and the second harmonic of at least some of the plurality of frequencies while the transducer is coupled to the nonlinear system; wherein measuring is performed by bouncing light from a laser off the cantilever and onto a photo-diode while interacting the tip with the sample; determining the form of a dynamical model to fit the measured data; and solving for a set of phenomenological parameters characterizing the dynamics of the nonlinear system, and wherein the method is used in microelectromechanical applications including accelerometers, stress sensors, nonlinear circuit components, or AFM.