This study explores how the damping coefficient affects vibration in small electric cars. By developing a mathematical model and simulating different damping coefficients, the authors found that this coefficient is crucial for controlling vehicle vibration, leading to a smoother and safer driving experience. Unlike traditional gasoline cars, small electric vehicles require different damping coefficients due to their distinct weight and structure. The study offers specific recommendations for optimizing damping coefficients in current electric car models, aiming to enhance user comfort and safety. This research is vital for improving small electric vehicles in Vietnam and supporting the shift to green transportation. Detailed findings are available in the full research paper.