Application of Alternating Harmonic Series

by Dalton Knowles

Submitted : Spring 2019

In this project a standard alternating series function is built with respect to time to best recreate the damped oscillatory movement of a guitar string. This is accomplished by using the values of the alternating series at every unit of time to decrease the value of the amplitude as the values switch between positive and negative numbers. The shape of the string itself is comprised in the sine and cosine formula (4) which, on its own, does not incorporate the decay of the string by external forces. Concluding the substitution of all the given and calculated values it is found a new variable “p” must be included in the alternating series to vary the speed of the amplitude. Without this value the motion dissipates too rapidly and must be accounted for as the external forces in a real string would allow it to vibrate for longer.

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