Shock Waves in Falling Coupled Harmonic Oscillators

TL;DR

This paper investigates shock wave propagation in falling coupled harmonic oscillators, providing exact and approximate solutions, and analyzing the shock wave width growth over time.

Contribution

It introduces exact and approximate analytical solutions for shock waves in falling harmonic oscillators, including Fourier and Airy function approaches.

Findings

Shock waves propagate upward in the system.

The bottom end remains stationary until shock arrival.

Shock wave width increases following a power law.

Abstract

Shock waves propagate in falling coupled harmonic oscillators. The bottom end of coupled harmonic oscillators does not fall downwards until a shock wave reaches the bottom end. The exact solution can be expressed by the Fourier series expansion, and an approximate solution can be expressed by the integral of the Airy function. The width of the shock wave increases slowly in accordance with a power law.