Abstract
Depending on the current position of the mass in different areas of the spring deformation during the oscillation process the values that determines the natural frequency of free continuous oscillations have opposite signs. It is defined by the change in the direction of acceleration of the mass in these areas, which makes it possible to determine a single inhomogeneous differential equation of the oscillation process in different areas of the movement of the mass. When the oscillation amplitude is much less than the static position of the mass, this inhomogeneous differential equation represents a homogeneous differential equation of free undamped oscillations.
Highlights
Depending on the current position of the mass in different areas of the spring deformation during the oscillation process the values that determines the natural frequency of free continuous oscillations have opposite signs
It is defined by the change in the direction of acceleration of the mass in these areas, which makes it possible to determine a single inhomogeneous differential equation of the oscillation process in different areas of the movement of the mass
When the oscillation amplitude is much less than the static position of the mass, this inhomogeneous differential equation represents a homogeneous differential equation of free undamped oscillations
Summary
При амплитуде колебаний намного меньше статического положения груза, это неоднородное дифференциальное уравнение вырождается в однородное дифференциальное уравнение свободных не затухающих колебаний. Свободные колебания массивного твердого тела на идеальной упругой пружине1 является классическим примером механической задачи, которая хорошо изучена, и корректно описана системой уравнений при колебаниях груза вблизи статического равновесия груза на деформированной пружине, когда амплитуда колебаний намного меньше величины деформации пружины при статическом равновесии груза [1, 2].
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