Oscilador harmônico com massa variável e a segunda lei de Newton

Abstract

Empregamos a segunda lei de Newton para descrever o sistema de oscilador com massa variável. Um aparato experimental para medir as oscilações e outros parâmetros importantesé montado e aqui descrito com a ajuda de equipamentos disponíveis comercialmente. Usando um modelo pré-concebido para tal sistema somos capazes de ajustar os resultados experimentais com boa concordância. Para realizarmos essa tarefa desenvolvemos um programa na linguagem C++ ao qual pode extrair os valores experimentais da amplitude do movimento oscilatório bem como rotacionar o sistema de coordenadas para separar o movimento translacional do movimento oscilatório. Palavras-chave: oscilador harmônico, massa variável, modos normais.We employ the Newton's second law to describe the variable mass oscillator system. We describe and set up an experimental apparatus in order to measure the oscillations and other parameters with the help of equipments available commercially. By using a preconceived model for such a system we are able to fit the experimental results with a good agreement. To accomplish this task we developed a C++ program which can extract the experimental values of the amplitude of the oscillatory movement as well as to rotate the coordinates system in order to set apart the translational movement from the oscillatory one.

Two helpful developments towards better understanding of adiabatic invariance in classical mechanics

“…For the one-dimensional harmonic oscilator there is only one action variable J, which is easily evaluated by equation (3) and coincides with the adiabatic invariant J = E ω , as expected [5]. Then, a further common doubt come to students: If we consider the oscillator's mass m also slowly varying in time [25,26], how can the adiabatic invariant be the same under slow variation of different parameters? The doubts deepen when apparently correct derivations by the elementary procedure discussed in the previous section lead to results other than J = E ω .…”