Answer: Vibrating String A string stretched between the two points and is plucked by

Chapter 8, Problem 93

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A string stretched between the two points (0,0) and (2,0) is plucked by displacing the string  \(h\)  units at its midpoint. The motion of the string is modeled by a Fourier Sine Series whose coefficients are given by

\(b_{n}=h \int_{0}^{1} x \sin \frac{n \pi x}{2} d x+h \int_{1}^{2}(-x+2) \sin \frac{n \pi x}{2} d x \).

Find \(b_{n}\)

Text Transcription:

h

b_n = h int_{0}^{1} x sin n pi x / 2 dx + h int_{1}^{2}(-x + 2) sin n pi x / 2 dx

b_n