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Unformatted text preview: Quiz 2 Solutions Kevin Setter November 6, 2009 Note: The correct solutions to parts 3 and 4 involve a subtlety that a Ph2a student is not expected to be able to get. Therefore, full credit was awarded to the naive solution to 3 and 4 described below. The correct solution is then described in 3 and 4. 1 At t = L/ 2 v , the string looks like Figure 1: Sketch of y ( x, 0). 2 At t = 0 the displacement is y ( x, 0) = ( 8 A L x, if 0 < x < L/ 8 , otherwise 3 At t = 0, the vertical string velocity is given by y t ( x, 0) = (- 8 Av L , if 0 < x < L/ 8 , otherwise (See 3 below for the correct answer.) 1 Ph2a Solutions Quiz 2 November 6, 2009 4 Using the trigonometric identity written in the statement of problem 7, we rewrite the Fourier expansion in the more tractable form y ( x,t ) = X n =1 A n cos( n t + n )sin n L x = X n =1 A n sin n L x cos( n t ) + B n sin n L x sin( n t ) where the phases n and the amplitudes A n are obtained from the coefficients A n , B n by ( A n = p ( A n ) 2 + (...
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This note was uploaded on 01/28/2011 for the course PH 2 taught by Professor Dudko during the Spring '09 term at UCSD.
- Spring '09