Normal Modes Simulation

A row of masses joined by springs can vibrate in special patterns called normal modes, in which every mass moves at the same frequency. Any motion of the system, however messy, is a mixture of these modes. A chain of N masses has N modes, from the slow one where all move together to the fast one where neighbours move opposite ways.

In this normal modes simulation you choose the number of masses in one dimension or a grid in two, set the amplitude and phase of each mode, and see transverse or longitudinal motion. It connects Oscillations and Waves in Class 11 to the standing waves on strings and in pipes, and to Olympiad problems.