npsm 새물리 New Physics : Sae Mulli

pISSN 0374-4914 eISSN 2289-0041


Research Paper

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

Published online October 30, 2020

Copyright © New Physics: Sae Mulli.

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


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

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

조화진동은 대학 물리학 과정에서 필수적으로 학습하는 주제이다. 통상적으로 이에 대한 교육은 하나의 진동자가 행하는 단순조화진동에서 시작하여 감쇄력과 외부의 조화력을 첨가하면서 진행한다. 이어서 진동자가 두개 이상 결합하면서 나타나는 운동을 통해서 진동의 정규 모드들과 공명 등을 학습한다. 그 후 진동계를 연속적인 매질로 확장하여 파동의 진행과 정상파 등을 공부한다. 본 논문은 Glow Script를 기반으로 VPython 언어를 사용하여 개발한 대화형 컴퓨터 프로그램을 소개하고자 한다. 이 도구를 통하여, 임의의 개수의 진동자들이 결합한 진동자계를 외부의 조화력이 강제로 운동을 시킬 때 나타나는 운동의 행태를 시각적으로 확인하고 그래프를 통하여 정량적으로 분석할 수 있다. 이로부터 진동의 정규 모드와 공명 그리고 파동의 정상파에 관한 개념 등을 확고히 할 수 있다.

Keywords: 물리 교육, 결합 진동자, 수치 시뮬레이션

Fig. 1. Captured screens at the initial setup phase (a) and during the execution (b) of the program 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).