The goal of this study is to dynamically simulate a turning-centre main spindle system utilizing the systems receptance coupling technique to determine the spindle system’s first three resonant frequencies in the event of transverse vibrations. The findings are then confirmed using the finite element technique using ANSYS software. The significance of analysing the spindle system described in this study is that it can be utilized to optimize the spindle system in terms of resonance frequencies for improved performance in terms of spindle vibration while the turning centre is in operation.