IYPT 2013, Задачи на турнира — Задача 4. Soliton

Problems for the 26th IYPT 2013

Епиграф

There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy
Shakespeare

Условие

Hand-drawn sketch of a row of pendula hanging from a horizontal axis and joined by strings; along the chain the pendula swing through a full turn, forming a travelling twist. An arrow labelled c shows the propagation direction, and a curved arrow labelled ω marks the rotation at the end of the chain.

A chain of similar pendula is mounted equidistantly along a horizontal axis, with adjacent pendula being connected with light strings. Each pendulum can rotate about the axis but can not move sideways (see figure). Investigate the propagation of a deflection along such a chain. What is the speed for a solitary wave, when each pendulum undergoes an entire 360º revolution?

Решение

Внимание: Непълно решение

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

Оригинал в Архива: 2013.pdf