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Continuation of the discussion of systems with infinite number of degrees of freedom, in particular where the oscillators are identical, harmonic, and connected only to their neighbors. In this session, we discuss a situation where the solution of the wave equation can best be described in terms of the superposition of normal modes (a mathematical technique known as Fourier analysis).
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- Fourier analysis of a system consisting of a taut string fixed at both ends which, before it is released, is stationary and has a rectangular shape. (0:29:27)
- A discussion of an alternative derivation of the same result using progressive waves reflected at both ends of the string. (0:04:41)
Fourier analysis of a system consisting of a taut string fixed at both ends which, before it is released, is stationary and has a rectangular shape.
A discussion of an alternative derivation of the same result using progressive waves reflected at both ends of the string.
Related Problems
Related Lectures in 8.03 Physics III: Vibrations and Waves Course
- Lecture 7: Symmetry, Infinite Number of Coupled Oscillators
- Lecture 9: Wave Equation, Standing Waves, Fourier Series