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Physics 8.03 Vibrations and Waves

Explore Fourier analysis techniques in vibrations and waves. Learn how to determine Fourier coefficients and add time dependence to the analysis. Includes information about upcoming exams and problem set due dates.

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Physics 8.03 Vibrations and Waves

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  1. Physics 8.03Vibrations and Waves Lecture 10Fourier Analysis

  2. Announcements for today • Problem Set #5 due Monday March 15 • Exam next Thursday, March 18 • Exam review? • No review • Monday 9pm • Monday 10pm • Tuesday 9pm • Tuesday 10pm

  3. Last time: • Normal modes in 2-D • Arbitrary motion  Superposition of  normal modes • Orthogonal functions  Fourier coefficients 

  4. Today • Fourier analysis continued • Time evolution added • Complete basis set

  5. Fourier expansion recipé • Start with superposition of all possible modes • Determine the simplest basis functions using • Boundary conditions • Symmetry • Initial condition • Determine the Fourier coefficients, Am and Bn, at t = 0 using initial deformation y(x , t = 0) and orthogonal functions • Add the time-dependence

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