# ESTUDO SOBRE EFICIENCIA DE RESOLUÇÃO NUMÉRICA DO FENÔMENO MASSA-MOLA

## Palavras-chave:

Error, Numerical methods, Differential equation, Mass-spring phenomenon## Resumo

The study of numerical methods is essential for the sciences, being that we often can’t solve

analytically the mathematical problems. However, these generate errors, in which they can often cause

catastrophic disasters if proper precautions are not taken. In this article, we will make a case study for the

mass-spring phenomenon. For purposes of comparison and demonstration of efficiency, we will solve

the problem by the numerical methods based on Taylor series, Euler First Order, Runge-Kutta Second

and Fourth Order, and by the classic analytic form. The theory about Taylor series allows us to only

estimate the order of magnitude of the error. In this case study, the error generated by each method

will be analyzed directly and compared by means of the relative error criterion, absolute and relative

amplitude. As a measure of quality, we will propose an adapted variation of the six-sigma quality control

system. We conclude that the method of Runge-Kutta Fourth Order is of excellent quality (“four sigma”)

under some conditions (step h of lengths 0.025).