Determining and Correctly Understanding the Damping Coefficient in Harmonic Oscillation Reduces the Calculation Volume and Modifies Knowledge for the Designer

The damping coefficient in engineering is an important issue. Currently, science uses computers to determine this coefficient. With a considerable amount of input data, solving is complicated. Therefore, manual calculation is an insurmountable challenge. This paper presents a valuable theory to determine the damping coefficient, simplifying the data entry process for processing through the computer. Thereby, the method saved effort and time. Determining the damping coefficient in theoretical mechanics is very difficult. So far, it has often been determined experimentally. Because all measurement methods have errors, the determination is even more difficult. When the number of objects that need to measure damping parameters in practice is large, the calculation and processing process takes more effort. The mathematical and physical theory used in the article has been around for a long time. However, these theories were applied to the problem in a completely new way and solved the problem fundamentally. The larger the calculation volume, the more damping included factors and the more meaningful this theory is. The approach also clarifies that the damping coefficient is a parameter that depends on stiffness and mass rather than an independent parameter in harmonic oscillation. This additional knowledge also contributes to understanding and applying this parameter's mathematical and physical nature in science and practice. At the same time, it also opens up completely new research directions.