Cilia are small but mighty hair-like organelles found on many types of cells, including those in the lungs and pancreas, as well as on single-celled organisms like protozoa. Motile cilia beat in coordinated patterns, while non-motile (primary) cilia act as sensors in cell signaling. When motile cilia beat together, they generate metachronal waves - crucial for many physiological processes. The synchronization that drives these waves has long been studied, with attention to both internal structure and external environment. My research explored the hydrodynamic interactions between a singular biological cilia and an artificial one. Simple models show that synchronization depends on factors like spacing, beat geometry (circular, elliptical, or asymmetric), and flexibility. I aimed to contribute to a more rigorous, quantitative model of hydrodynamic synchronization, focusing on how the beating phase influences coupling.