IYPT 2018, Задачи на турнира — Задача 11. Azimuthal-Radial Pendulum

Problems for the 31st IYPT 2018

Release note and epigraph

Released by the IOC on July 13th, 2017

The originator of a new concept finds, as a rule, that it is much more difficult to find out why other people do not understand him, than it was to discover the new truth.

Hermann von Helmholtz

Условие

Fix one end of a horizontal elastic rod to a rigid stand. Support the other end of the rod with a taut string to avoid vertical deflection and suspend a bob from it on another string (see figure). In the resulting pendulum the radial oscillations (parallel to the rod) can spontaneously convert into azimuthal oscillations (perpendicular to the rod) and vice versa. Investigate the phenomenon.

Perspective drawing of the pendulum: a vertical rod stands on a blue square base; a horizontal elastic rod is fixed to the stand and supported at its free end by a taut string running up to the top of the stand; a bob hangs from the rod end on another string; a pale blue horizontal plane marks the rod level, with dashed lines and arcs indicating the radial and azimuthal oscillation directions.

Решение

Внимание: Непълно решение

Това е открита изследователска задача — официални решения не се публикуват.

Оригинал в Архива: 2018.pdf