A string stretched between the two points and is plucked by displacing the string units
Chapter 8, Problem 113(choose chapter or problem)
Vibrating String 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:
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
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