Decomposition Model and Extension of Spring Pendulum Systems in the 21st Century: A Systematic Literature Review

Abstract

A spring pendulum is a mechanical system that describes the reciprocating motion of a mass suspended on a spring around an equilibrium point. The system consists of a spring with certain elasticity characteristics and a fulcrum to which the spring is attached. When the mass is pulled from its equilibrium position, the spring generates a restoring force proportional to the distance of displacement, inducing the mass to move periodically. Spring pendulum systems have seen frequent development in the design of mechanical systems that require high-precision vibration control. This study examines developments in system expansion and equation decomposition models of spring pendulums by conducting a Systematic Literature Review (SLR) of 36 pertinent articles from Scopus and Google Scholar (2000–2024). The main focus of the research lies on the expansion of the basic spring pendulum system through various modifications, which is the dominant topic in the review. The most popular technique for resolving the system's equations of motion is breaking down the equations using analytical mathematical formulations, particularly the Lagrangian method, which refers to the theoretical derivation of equations of motion through well-known mathematical frameworks like Lagrangian and Hamiltonian mechanics. The findings provide deep insights for the development of mathematical models as well as a comprehensive overview of the development of spring pendulum research. The implications of this research can contribute to innovations in engineering, physics, and other related disciplines.