In section 3.9, we showed how Fourier series could be used to represent a periodic function. Here we wish to apply that analysis to a vibrating string. Assume that a string of length l of mass per unit length μ. is stretched horizontally between two supports and held with tension F0. Assume that the middle of the string is displaced a distance a (where a «l) in the vertical direction. When the string is released, it vibrates in a standing wave pattern. Use Fourier analysis to calculate the pattern of vibration as a function of time (Figure P 11.29), that is calculate the Fourier coefficients of the series needed to describe the motion.
Figure
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