An Alternative Approach To The Vibrating String Problem

An Alternative Approach to the Vibrating String Problem
Author: Chew, James
College Mathematics Journal, Vol. 12, no. 2, pp. 147-149, 1981.

This article presents a method of solving the wave equation through basic properties of functions and careful use of the initial and boundary conditions. The approach takes an arbitrary function that satisfies the wave equation and show (through familiar and simple mathematics) that it must be equal to a linear combination of sine and cosine function of a specific form. The procedure could be a useful exercise in mathematical reasoning and in determining what combination of functions are solution to a given differential equation. (Summary by Ben Murphy, Pomona College '13)

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