Squeeze film damping is a significant phenomenon in various engineering fields, including microelectromechanical systems (MEMS) and rotating machinery. This study focuses on audio MEMS transducers, where squeeze film damping is crucial for high-quality audio performance. The research aims to assess the effectiveness and precision of the harmonic balance method versus the widely used time integration method in modeling the complex dynamics and predicting total harmonic distortion. Through numerical experiments, the study compares the outcomes of both methods across different quality factors and amplitudes. The results will enhance the understanding of each method's advantages and limitations, aiding researchers and engineers in choosing the most suitable numerical technique for analyzing time-periodic nonlinear squeeze film damping issues.