Mathematical modeling is a fundamental tool in engineering and the sciences. Models capture the behavior of real systems through mathematical and physical relationships, enabling analysis, prediction, and optimization. Depending on the application, models can range from simple and computationally efficient to highly detailed and precise for critical systems. Dynamic behavior is often described by differential equations, and model parameters - such as stiffness or damping - are calibrated using experimental data to minimize errors and ensure accurate representation of real-world performance.