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
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...
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...
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...
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.
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...
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> =...
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
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...
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...
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?
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...