Frequency lock-in-induced deadband phenomena are major problems of ring laser gyroscopes (RLGs), which deteriorate linear responses to changes in the applied rotation rate. In this work, the frequency lock-in phenomenon occurring in the RLG was successfully investigated by compensating for the Sagnac effect through frequency analysis using a newly defined error function. Integrative and generalized viewpoints from the analyzed results provide new possibilities for relevant performance improvements of optical gyroscopes, as well as a deeper understanding of locked states in principle aspects.