Ecuaciones diferenciales de segundo orden y su aplicación a las vibraciones mecánicas

Abstract

The aim of this research work was to generate a document used as a reference for the understanding and resolution of second order differential equations and their application to mechanical vibrations, specifically to the spring-mass system. For the development of the study, bibliographic-documentary research with a qualitative approach and descriptive level was considered, the collection and analysis of the information was structured through a process of documentary search, identification, collection and selection of texts and articles available on the Internet and related to the proposed topic. The result obtained was a study guide called: ”Second Order Differential Equations and their Application to Mechanical Vibrations”, which describes in a clear and concise way the methods and resolution of the first and second order differential equations, as well as the application to the spring-mass system. At the end of this research, it was concluded that the differential equations subject, belonging to the Mathematics degree program requires a thorough and detailed study to deepen in applicative topics, in addition to the understanding of definitions, theorems, propositions and demonstrations. It is recommended to continue the study on the applications of second and higher order differential equations that can be complemented with Laplace transforms to ease the calculations.