RELATIONS BETWEEN PERIODS AND AMPUTUDES OF PERIODIC SOLUTIONS OF x +g(x) =0

摘要

The period of the periodic motion described by the equation in the title -varies with its amplitude or amplitude of velocity, the problem studied in the present report is to find the relations between the period and the amplitude or the amplitude of velocity in such a form that, from these relations, it is possib to determine the function g(x) which yields periodic motions whose period ma vary in the arbitrary perscribed way with the amplitude or the amplitude of velocity. The half-periods and the Half-amplitudes are also brought into question. In illustration, there is computed the function g(x) which yields periodic motions whose period may vary linearly with the amplitude.