Problems for
Intermediate Methods in Theoretical Physics

Edward F. Redish

Time dependence from Fourier series

In lecture we demonstrated that the shape of a string plucked in the center:

could be expanded in a Fourier series

with Fourier coefficients:

(a) If at time t = 0 the string is plucked in the center so that when it is released:

then find an expression that will give the shape of the string for all times, y(x, t).

(b) Assuming that it is OK to ignore any damping or internal friction, will the string ever resume its original shape after it has been released? If so, will it do it regularly? If so, with what period? Explain carefully how you came to your conclusion.

(c) Suppose that instead of plucking the string in the center, you plucked it 1/4 of the way from one end to the other. Answer the same question as in (b).

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Edward F. Redish
Department of Physics
University of Maryland
College Park, MD 20742
Phone: (301) 405-6120
Email: redish@umd.edu

Last revision 14. November, 2004.