Aeroelastic wing flutter plays a crucial role in the field of aerospace engineering, as it addresses a significant concern in aircraft design and safety. Flutter refers to the self-excited oscillations that can occur in an aircraft’s wings when subjected to certain aerodynamic forces and structural dynamics. These oscillations can lead to potentially catastrophic consequences if not properly understood and addressed. Understanding aeroelastic wing flutter is essential to ensure the structural integrity, stability, and performance of aircraft. It helps to identify critical conditions, design robust wings, and develop strategies to mitigate or suppress flutter, ultimately contributing to safer and more efficient air transportation. This technical paper presents an investigation on a system of equations, incorporating structural damping, and explores the solution to the corresponding eigenvalue problem across a range of speeds. The primary objective in this research is to analyze and visualize the trends of Vω (eigenvalue) and Vg (system speed), by writing a code in MATLAB. The code facilitates numerical solution of the system equations, allowing for the study of damping effects on the system's behavior. By systematically varying the speed parameter, the resulting eigenvalues and system speeds are obtained and plotted to provide insights into the system's dynamic characteristics.