Simulating longitudinal vibrations of coupled oscillator using the fourth-order Runge–Kutta method by programming spreadsheet

Abstract This paper presents a simple way of simulating the motion of two oscillators coupled via springs. A linear model using Hooke’s law describes the motion of a coupled oscillator through a set of two coupled second-order linear differential equations. A spreadsheet is programmed to obtain the numerical solutions of coupled differential equations using the fourth-order Runge–Kutta method. The main thrust behind programming the spreadsheet is to solve the differential equations for a physical system under different initial condition and to understand the motion of coupled masses graphically. The programmed spreadsheet can also be modified to include damping in the system and visualize a damped dynamical system. The algorithm developed for programming presents the use of inbuilt functions of the spreadsheet and is user-friendly, especially for those who are not familiar with the spreadsheets. Simulations of the coupled oscillator would help students to visualize the effect of variation of different parameters, such as mass, initial velocity, spring constant, and damping factor, on the motion of coupled oscillators.