Equações Diferenciais de Segunda Ordem e Aplicações

Abstract

This work addresses second-order ordinary differential equations (ODEs), with an emphasis on their applications in physical systems such as the mass-spring system and electrical LRC circuits. Initially, the methods for solving these equations are discussed, both for homogeneous and non-homogeneous systems, with the presentation of general and particular solutions. In the case of the mass-spring system, the differential equation describes oscillatory motion, taking into account forces such as friction and the restoring force of the spring. As for the LRC circuit, ODEs model the behavior of current and charge in the circuit, influenced by resistance, inductance, and capacitance. The study explores how these mathematical models are essential for understanding and predicting the dynamic behavior of these systems, emphasizing their applications in engineering and physics. The analysis highlights the importance of second-order ODEs in describing phenomena of oscillation and damping, providing a solid foundation for understanding real systems.