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(a) A cord of length L is rigidly attached at both ends and is plucked to a height h at a point 1/3 from one end and let it go. Show that the displacement y at any distance x along the string at time t in the subsequent motion is given by y=3^(5/2)/2pi^2[sin pix/L cos pivt/L + 1/4sin 2pix/L cos 2pivt/L - 1/16sin 4pix/L cos 4pivt/L...] (b) and that the third, sixth and ninth harmonics are absent. |
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