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Physics 8.03 Vibrations and Waves

Physics 8.03 Vibrations and Waves. Lecture 10 Fourier Analysis. 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. Last time:. Normal modes in 2-D

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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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