A study was conducted to analyze the dynamic behavior of a two-degree-of-freedom (2-DOF) passive quarter-car suspension model to understand vehicle vibration and ride comfort characteristics. The equations of motion were derived to determine the system’s natural frequencies for both the body and wheel modes. MATLAB simulations were then used to evaluate the vehicle’s response to a sinusoidal road disturbance. A parametric analysis investigated the effects of varying damping and stiffness on the sprung mass displacement and acceleration. The results showed that increased damping reduces vibration but eventually saturates, while excessive stiffness can negatively affect ride comfort, highlighting the need for optimal suspension parameter tuning.