pISSN 0374-4914 eISSN 2289-0041

## Research Paper

New Phys.: Sae Mulli 2020; 70: 871-879

Published online October 30, 2020 https://doi.org/10.3938/NPSM.70.871

## Interactive Simulation of the Motions of a Linear Mass-Spring Chain with VPython

Chang-Bae KIM*, Dong Ryeol LEE, Hee-Sang KIM, in-Seok CHUNG, Myung Ki CHEOUN, Yunsang LEE, Jin-Min KIM, Taehoon LEE, Hangmo YI, Se Young PARK, Nammee KIM, Doris Yangsoo KIM, Hyunhee CHOI

Physics Department and Research Institute for Origin of Matter and Evolution of Galaxies, Soongsil University, Seoul 06978, Korea

Correspondence to:cbkim@ssu.ac.kr

Received: June 1, 2020; Revised: August 5, 2020; Accepted: August 21, 2020

### Abstract

A computer program written in the VPython language on the Glow Script platform is developed with a view to aiding the study of vibrations and the waves. It simulates the forced motions of coupled oscillators of arbitrarily large number. Understanding the harmonic oscillations of physical systems underlies the core curriculum of college physics. It normally starts with the simple harmonic oscillation of a single oscillator and, afterwards, adds damping and external harmonic forcing. More than one coupled oscillators are, then, introduced and they give ways for understanding waves in continuous media as the number of oscillators becomes large. The reported product visualizes the motions of coupled oscillators and enhance the comprehension of such concepts as the normal modes of vibration and stationary waves.

Keywords: Physics education, Coupled oscillators, Numerical simulation

### Figures

Fig. 1. Captured screens at the initial setup phase (a) and during the execution (b) of the program FCO.py: The distance between two walls is $1$m, the total mass of the all objects $0.25$kg, the number of the objects $N=10$, the spring constant $k=6.0$N/m, the amplitude and the frequency of the external force $f_{\rm ext}$ is $5.455\times10^{-4}$N and $\nu_{\rm f}=0.70$Hz, respectively. The rightmost spring is fixed to the wall. The figure with black background in (a) shows the oscillating system where each orange box represents the object and the cyan cylinder visualizes the spring. In the corresponding figure in (b) the oscillating objects are hidden in the display for better view and the colors of the springs change in accordance to their length after $23.09$ seconds of motion. Red or yellow color means that the spring is either contracted or stretched, respectively, while the color gray denotes that the length of the spring is changed little. Two graphs in (b) show the displacements of $N$ bodies (top figure) and the energies, kinetic (green), potential (blue), mechanical (red) and externally supplied (orange), in time (bottom figure).