Dynamic Analysis of an Undamped Two-Degree-of-Freedom Vibration System

Abstract

This research investigates the dynamic characteristics of an undamped two-degree-of-freedom (2DOF) mechanical vibration system subjected to free vibrations. The study aims to explore the modal response, natural frequencies, and mode shapes of a system consisting of two masses connected by linear springs without energy dissipation. Using classical analytical methods and matrix formulations, the equations of motion are derived and solved to obtain the system’s characteristic equation. The resulting natural frequencies and corresponding mode shapes are analyzed to understand coupled motion behavior and resonance conditions. The influence of mass and stiffness ratio on dynamic response is examined through parametric studies. The results provide insight into the critical role of modal coupling in multi-degree-of-freedom systems, laying the groundwork for further studies in vibration isolation, mechanical design, and structural dynamics. This work is relevant for engineers and researchers involved in mechanical systems, structural health monitoring, and dynamic control of coupled mechanical components.

Cite as:

A. D. Awasare, & Ingwale Omkar. (2025). Dynamic Analysis of an Undamped Two-Degree-of-Freedom Vibration System. Research and Reviews: Journal of Mechanics and Machines, 8(2), 18–23. 

https://doi.org/10.5281/zenodo.15638965