Modeling Vibrating Strings Using Ordinary Differential Equations
0Day 1 | 8:00 PM–8:30 PM
"Modeling Vibrating Strings Using Ordinary Differential Equations"
Presented by:
Mihaela-Cristina Drignei, University of Pittsburgh at Bradford, Bradford PA USA
https://qubeshub.org/community/groups/simiode/expo/2025
Abstract: This introductory talk will demonstrate how a physical problem can be naturally addressed using ordinary differential equations. Specifically, the modeling of a vibrating elastic string under various constraints at its end points is presented. The assumptions made are as follows: the vibrations occur only vertically; they are infinitesimal; the string has negligible weight. Basic calculus concepts, such as the slope of a curve, and elementary physics concepts, such as Newton's second law of motion and Hooke's law for elastic springs are used in developing the ordinary differential equation model with corresponding boundary conditions. Furthermore, connections between the vibrating string model and the direct/inverse Sturm-Liouville problems are briefly discussed.