Mathematics Lecture Series

Mathematics Lecture Series

Postby staing » Tue Nov 13, 2012 9:23 am

Mathematics Lecture Series, Fall 2012
Fresno State

Dr. Steve Cox
Rice University

“One Can Hear the Composition of a String: Experiments with an Inverse Eigenvalue Problem”

Friday, November 16, 2012
from 4:00 p.m. to 5:00 p.m.
Science 145

We consider a case study in Inquiry Based Learning. To what extent do the vibrations of a mechanical system reveal its composition? Despite innumerable applications and mathematical elegance, this question often slips through those cracks that separate undergraduate courses in mechanics, differential equations, and linear algebra. We address this omission by detailing a classical finite dimensional example: the use of frequencies of vibration to recover positions and masses of beads vibrating on a string. First we derive the equations of motion, then compare the eigenvalues of the model against vibration data measured from our laboratory's monochord. More challenging is the recovery of masses and positions of the beads from spectral data. After presenting a solution, based on orthogonal polynomials, in a manner suitable for advanced undergraduates, we confirm its efficacy through physical experiment and discuss our students' ability to synthesize analysis, numerics and experiment.

For further information, please contact Dr. Tamas Forgacs at (559) 278-4907 or e-mail
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Department of Earth and Environmental Sciences
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