A limit cycle phenomenon refers to an isolated closed trajectory of the states of a non-linear dynamic system in a two-dimensional phase space. Line start interior permanent magnet (LSIPM) motors often experience limit cycles due to variations in the load or supply, causing sustained oscillations in the drive system. This article presents an analysis of the limit cycle phenomenon in LSIPM motors, and proposes a method to detect its existence in the system using the stator current signal analysis in time-frequency domain. The proposed method is first validated by conducting the finite element analysis for a three-phase 1-HP 4-pole LSIPM motor under various limit cycle induced operating conditions. It is further validated experimentally in the lab using a 1-HP LSIPM motor drive. Both simulation and experimental results indicate that the proposed method can successfully detect the existence of limit cycles in LSIPM motor drives.