We describe the motion of a droplet on a textured ratchet track using a non-linear resonator model. A textured ratchet track is composed of semi-circular pillar array that induces a net surface tension gradient on a droplet placed on it. When a vertical vibration is applied, hysteresis is overcome, and the droplet moves towards the local lower energy barrier; however, due to the repetitive structure of texture, it keeps moving until the end of the track. The droplet motion depends on the amplitude and frequency of the vertical oscillation, and this dependence is nonlinear. Therefore, finding a fully analytical solution to represent this motion is not trivial. Consequently, the droplet motion still remains as a topic that needs further investigation. In this study we elaborate on the utility of double-pendulum as a basis for modeling the droplet motion on surfaces. Similar to the droplet motion, resonators, such as double pendulum, are simple, yet non-linear systems. Moreover, inverted double pendulum motion has key characteristics such as two phase motion and double peak motion, which are also observed in the droplet motion on textured ratchets. In this thesis, data processing models are developed to highlight the similarity between these two systems both qualitatively and quantitatively. After establishing this comparison, a model is proposed that utilizes an inverted double pendulum mounted on a moving cart to successfully simulate the motion of a droplet on a ratchet track. This methodology will lead to developing an accurate droplet-motion modeling approach which will be useful to understand droplet dynamics in more depth.