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  1. J

    Fourier Series of an Odd Piecewise function

    Homework Statement Fourier Series of the following function f(x). f(x) is -1 for -.5<x<0 f(x) is 1 for 0<x<.5 Homework Equations b_{n} = \frac{1}{L}\int^{L}_{-L}f(x)sin(nπx/L)dx Where L is half the period. The Attempt at a Solution Graphing the solution, I know that it is odd, which is...
  2. J

    Relativistic motion in a particle accelerator: Rate of Energy Loss

    Mother of mercy, that's it! Solving for Kinetic Energy to get gamma, then solving for v using the equation I got, then plugging it all into the last equation got me my answer. It also helped me out on the two questions after the one I posted, where my velocities were all just a hair below the...
  3. J

    Relativistic motion in a particle accelerator: Rate of Energy Loss

    Homework Statement (a) Consider a 10-Mev proton in a cyclotron of radius .5m. Use the formula (F1) to calculate the rate of energy loss in eV/s due to radiation. (b) Suppose that we tried to produce electrons with the same kinetic energy in a circular machine of the same radius. In this case...
  4. J

    Fourier Coefficients of an Even Function

    ((Just a side note, sorry about posting this thread in the wrong board. I couldn't decide which one to post it in between the Introductory and the Advanced Physics boards and figured it might be upper-level introductory. Thank you for correcting my error. Also, I'll make the equations a bit...
  5. J

    Fourier Coefficients of an Even Function

    Given F(x) = \sum^{∞}_{n=1} A_{n}cos(\frac{2πnx}{λ}) Considering we're solving for A_{n}, I figure it couldn't be used in the integral (given in the original post). So: An = \frac{2}{λ}\int^{λ}_{0} F(x)cos(\frac{2πnx}{λ}) dx = \frac{2}{λ}\int^{λ}_{0} cos(\frac{2πnx}{λ})*cos(\frac{2πnx}{λ}) dx...
  6. J

    Fourier Coefficients of an Even Function

    Alright. Given that the function F(x) is an even function, the equations will only deal with cosines. Using the equation I was given in this book and the equations Matt gave me, my end result is: My integrals were: An = \frac{2}{λ}\int^{λ}_{0}cos2(\frac{2πnx}{λ})dx and An =...
  7. J

    Fourier Coefficients of an Even Function

    Modern Physics for Scientists and Engineers, 2nd Edition. Authors are John Taylor, Chris D. Zafiratos, and Michael A. Dubson. Chapter 6, problem #32. I figure more information than necessary is better than too little information.
  8. J

    Fourier Coefficients of an Even Function

    Homework Statement For a given periodic function F(x), the coefficients An of its Fourier expansion can be found using the formulas (Form1) and (Form2). Consider a periodic square pulse and verify that the Fourier coefficients are as claimed: An =(\frac{2}{πn})sin(\frac{πan}{λ}) for n≥1 and...
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