Numerical Solutions to Vibrations of Bars

The acoustic problem of vibrations of bars is usually solved with graphic methods and most books that have these equations in them just mention that you could use the Newton-Raphson method to solve it. The approach in this article is different. This article uses the NuGet symbolic mathematics package MathNet.Symbolics together with my C# implementation of the Jenkin-Traub root-finding algorithm of polynomials to solve these problems.