About the Simulation

The Spring Chain program is designed to simulate a system of coupled masses attached by springs and moving in one dimension. The positions and velocities of the masses can be manipulated in various ways to allow the user to model a variety of systems. This simulation uses the Fourth Order Runge Kutta method to solve the differential equations governing the motion of the particles.

Spring Chain displays its data in 3 graphs on the screen. The bottom graph shows an animation of the masses as they move in the system. It is important to note that the animation represents vertically the horizontal movement of the particles in the system. The top left graph shows the position as a function of time of the “particle of interest”. This particle’s identity is denoted by the title of the two smaller graphs, and is marked by a hollow circle on the animation graph at the bottom. The third set of axes, located in the top right corner of the application, shows a phase space graph for the same “particle of interest”. This phase space graph plots velocity as a function of position for the particle.

Spring Chain includes among its built in capabilities the ability to inspect and manipulate data on either of the smaller top two graphs, as well as the ability to perform a Fourier transform on the data in the position vs. time graph for the particle of interest. The “Graph Inspector” can be invoked by right clicking on either of the two graphs, and the Fourier analysis can be chosen from the main menu, or by left-clicking on the position vs. time graph.

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Spring Chain

Written by:

Under the supervision of:

Davidson College

Physics 396

February 29,1996