Menstruation is a finely-controlled cycle that responds to the prevailing endocrine and paracrine environment. However, social stigma has led to inadequate menstrual literacy, both among academics and the larger public. The poorly understood mechanisms of menstruation ultimately lead to suboptimal healthcare treatment and services for biological females, culminating in a physical, financial, and emotional burden. Various hormones signal the beginning and end of each stage of menstruation. In particular, luteinizing hormone (LH) is a major player in ovulation, corpus luteum function, and the stimulation of other key hormones. A LH model could be used to understand the larger control system of menstruation if analyzed in conjunction with models for other major hormones (e.g., FSH, progesterone, and GnRH). Thus, exploring a smaller subsection of LH dynamics within the larger control system of menstruation can lead to a greater understanding of menstruation, contributing towards therapeutics and research for women's health. Using parameters and kinetic equations in the existing body of literature, a transfer function was derived to model LH dynamics. Analysis of system stability reveals overdamped dynamics in LH sensitization at baseline, and underdamped mildly resonant dynamics at the peak of the menstrual cycle, the strength of which depends on the values of the rate constants of LH receptor formation, binding, and desensitization.