Single Degree of Freedom Vibratory System - MATLAB Modeling and Simulation

A Single Degree of Freedom (SDOF) vibratory system refers to a mechanical system that possesses only one degree of freedom during vibration, meaning it can only oscillate in one possible direction. The mathematical model of this system can be described using a second-order ordinary differential equation. To better understand and analyze this system, MATLAB can be employed for modeling and simulation through numerical integration methods like ODE45. Using MATLAB modeling, we can obtain numerical solutions for the vibration equation of the SDOF system under different parameters. The implementation typically involves defining the system parameters (mass, damping coefficient, spring constant) and solving the differential equation using built-in solvers. Furthermore, by quantitatively describing the vibration process and analyzing frequency-amplitude characteristics through FFT analysis and plotting functions, we can gain deeper insights into the system's vibrational behavior and characteristics. In mathematical simulation experiments, various parameter values such as elastic modulus and damping coefficients can be modified to study their effects on the vibratory system. These experiments, implemented through parameter sweeping scripts and visualization tools like plot and subplot functions, enable comprehensive understanding of SDOF system's vibrational properties and behaviors, providing a solid foundation for subsequent research studies.