Damped simple harmonic motion (SHM) refers to the oscillatory behavior of a system in which a restoring force proportional to the displacement acts against a damping force that opposes the motion. This abstract explores the characteristics of damped SHM and its applications across various fields. We developed into the mathematical representation of damped SHM, discussing factors affecting the damping coefficient and its impact on the motion's amplitude and frequency. Additionally, we explore practical applications of damped and forced SHM. The abstract concludes by highlighting the significance of understanding damped SHM's principles in optimizing designs and enhancing system performance across different industries.