Computer Graphics for the Vibrating String

Computer Graphics for the Vibrating String

Author: Howard Lewis Penn

The College Mathematics Journal. Vol. 17, No. 1 (Jan., 1986), pp. 79-89.

Published by: Mathematical Association of America.

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Tag(s): Other topics in differential equations

Abstract. This paper was borne of Dr. Penn’s efforts to assign practicality to the work that his introductory differential equations students were doing as it relates to separation of variables to arrive at a solution to a differential equation, as well as the resulting series. He thought it expedient to use computer graphics to display the sum of the first few terms of the series expansion, a technically enlightening and visually appealing exercise. I enjoyed reviewing this paper because of how genuinely useful it is to associate the graph of a vibrating string with the drawn-out calculations of series sums. The ability to easily alter the initial conditions and make simplifying assumptions (i.e. the string has uniform density, the only force acting on the string is a uniform tension, and that initial displacement is so insignificant that each point on the string only moves vertically), makes for a model that is simple to operate and produce. This point is key because in our differential equations course this semester, I have found that models simplify challenging concepts in a way that initially allows me to understand general trends and subsequently understand the nuances of a system. I see that so clearly when I use SAGE math cloud for homework assignment requiring graphical models for predator-prey systems or for solutions to 2nd order linear systems. Toluwani Soares, Stephen F. Austin University, May 3, 2017.

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