Recent content by Bestphysics112

  1. B

    Find potential within a pipe using Laplace's equation

    If I follow the steps illustrated in post 3 but instead solve for d, I obtain -Csin(ak)=Csin(ak), so two possibility is C=0 or sin(ak)=0, so k=n*pi/a for this instance
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    Find potential within a pipe using Laplace's equation

    C need not be zero as well, so there must be another way to determine coefficients
  3. B

    Find potential within a pipe using Laplace's equation

    How does this fact help me in determining which (C or Do) is 0? Sorry for all the questions!
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    Find potential within a pipe using Laplace's equation

    I think I see what your point is. The other possibility would be that cos(ak) = 0, meaning k = n*pi/(2a)
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    Find potential within a pipe using Laplace's equation

    Either x = 0 or y = 0 Edit. I think I see what your point is. The other possibility would be that cos(ak) = 0, meaning k = n*pi/(2a)
  6. B

    Find potential within a pipe using Laplace's equation

    Another possibility is D=0? I'm unsure of what else it could be
  7. B

    Find potential within a pipe using Laplace's equation

    If I do the same but instead solve for C, I can find that C= -C.
  8. B

    Find potential within a pipe using Laplace's equation

    My reason is as follows - If I plug y = a into (Csin(ky)+Dcos(ky)), I can solve for C. Then if I plug in y = -a and my value for C, I can get -Dcos(ak) = Dcos(ak) (because sin is odd function and cos is even function) I'm not sure if my reasoning is correct so feedback is appreciated. I'm not...
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    Find potential within a pipe using Laplace's equation

    Homework Statement Hello, I'm trying to solve laplaces equation to find a solution for the potential in a pipe with the given boundary conditions: at x=b, V=V_0 at x= -b, V = -V_0 at y=a, V=0 at y=-a, V=0 (Assume this configuration is centered on the origin, pipe as dimensions -b<=x<=b...
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    Average energy of a damped driven oscillator

    After re reading my textbook I was able to get the correct answer
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    Change of variables formula

    I got the answer! Thank you!. However, If i wanted to solve it with the integral in dxdy, would i need to use two integrals?
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    Change of variables formula

    . I Evaluated this and x = 2y-6 and x = 2y - 12 ?
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    Change of variables formula

    No problem man! I initially tried setting the points I found as the limits of integration but then realized that I couldn't do that. After I plotted the points I found I saw that they formed a rhombus. So I found an equation for x in terms of y and set it up as follows...
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    Change of variables formula

    Why would I use the change of variables theorem to compute an integral in the xy plane? Sorry if this sounded too demanding but I've been staring at this problem for quite some time now.
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    Change of variables formula

    Homework Statement Homework Equations N/A The Attempt at a Solution I solved part a. I got an answer of 140. For part b, however, I am stuck. I came up with a set of points for D in the xy plane [(0,3)(0,6)(4,5)(4,8)] giving me a rhombus. How do i integrate this? I tried to split up the...
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