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  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
  2. B

    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!
  4. B

    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)
  5. B

    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...
  9. B

    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...
  10. B

    Average energy of a damped driven oscillator

    After re reading my textbook I was able to get the correct answer
  11. B

    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?
  12. B

    Change of variables formula

    . I Evaluated this and x = 2y-6 and x = 2y - 12 ?
  13. B

    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.
  15. B

    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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    Average energy of a damped driven oscillator

    Homework Statement http://imgur.com/a/lv6Uo Homework Equations Look below The Attempt at a Solution I was unsure where to start. I thought that parseval's theorem may be helpful. I know the Potential energy is equivalent to .5kx^2 and T will be the integral of the force. So i have $$<E> =...
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    Recast a given vector field F in cylindrical coordinates

    I don't have my homework with me, but I forgot to edit my post with the answer I got. The ez terms canceled
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    Recast a given vector field F in cylindrical coordinates

    Hello! Sorry I just saw this reply. As an answer, I got (rcos(θ)sin(θ)er +rcos2(θ)eθ +(2cos(θ)sin(θ)z+ 2sin(θ)cos(θ)z)ez Is this answer correct? Edit- Yes! I figured out my mistake and I got an equivalent answer. Thank you for the help Charles
  19. B

    Recast a given vector field F in cylindrical coordinates

    Homework Statement F(x,y,z) = xzi Homework Equations N/A The Attempt at a Solution I just said that x = rcos(θ) so F(r,θ,z) = rcos(θ)z. Is this correct? Beaucse I am also asked to find curl of F in Cartesian coordinates and compare to curl of F in cylindrical coordinates. For Curl of F in...
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    Unit vector perpendicular to the level curve at point

    Oh that makes much more sense. Thank you.
  21. B

    Unit vector perpendicular to the level curve at point

    No problem at all. I just wasn't sure what a level curve was.
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    Unit vector perpendicular to the level curve at point

    Homework Statement Find the unit vector perpendicular to the level curve of f(x,y) = x2y-10xy-9y2 at (2,-1) Homework Equations Gradient The Attempt at a Solution I'm not sure what it's asking. Wouldn't this just be the gradient of f(x,y) evaluated at (2,-1) then normalized? or am I missing...
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    Find vector parallel to two planes

    Thanks. Is LaTeX necessary for this forum? I will probably ask some questions in the physics sections soon and was wondering what formatting is preferred. Also how do i close this thread?
  24. B

    Find vector parallel to two planes

    Homework Statement Find unit vector(s) that are parallel to both of the planes 6x + y + z = 1 and x − y − z = 0 . Homework Equations N/A The Attempt at a Solution OK. So here is my reasoning - I find the normal of both the given planes and find the cross product between the vectors. The...
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