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1. ### Taylor Series : How to determine coefficient

I think the issue is that we can't find the link to click on in the first place. Nothing in your original statement contains a hyperlink - it's all just plaintext. Unless I'm starting to go blind.
2. ### Help Needed: Solving a Proof in Algebra

Ah, I had been incorrectly stating that 2^n + 2^n = 2^2n instead of 2*2^n = 2^n+1. Thanks for the help, sorry about the algebra error.
3. ### Help Needed: Solving a Proof in Algebra

Right, so isn't 2*(2^n) = 2^(n+1) ? But then I end up with 2^(2n) = 2^(n+1) which eventually leads to n = 1, yes?
4. ### Help Needed: Solving a Proof in Algebra

Greetings, It's been awhile since I've done induction or proofs in general, but I could not figure out where I went wrong on this one for the life of me. If anyone has an idea it would be much appreciated. I've uploaded a picture of the problem in the book as well as of my work. I thought I...
5. ### Equation describing a string on an elastic foundation

So, if wn2<0, does my T(t) then become T(t)=aewn2t+be-wn2t meaning that my total equation will become: u(x,t)=B0+\sum(ae^{w^{2}_{n}t}+be^{-w^{2}_{n}t})Bsin(npix/l) I'm not sure if that is entirely correct, and if it is, this is the point where I get stuck at. I'm just not quite sure what...
6. ### Equation describing a string on an elastic foundation

Ah, thank you very much for you help. I just have one more question involving the stability of the eigenfrequencies. Does the stability depend on the sign of the eigenfrequency? Such as if our eigenfrequency is w2n=w20-c2k2n, then if c2k2n > w20 we have stability or does it work differently...
7. ### Equation describing a string on an elastic foundation

Hum, do you mind telling me where I went wrong on my kn value? This is how I solved for it: if kn2 > 0 Then X(x,t) = Acosh(kx)+Bsinh(kx) X'(x,t) = 0 = -Aksinh(kx)+Bkcosh(kx) X'(0,t)= Bkcosh(0) and since kn2 > 0, B = 0 X'(l,t) = -Aksinh(kl) = 0 so kn2 = 0, but kn2...
8. ### Equation describing a string on an elastic foundation

Ah, I do see where I made the sign mistake. I forgot to carry the negative sign through when I transferred T(w^{2}_{0}-k^{2}_{n}c^{2}) to the other side. As to eigenfrequencies, I'm afraid I don't quite understand their role or how they're derived. We didn't discuss normal modes in class at...
9. ### Equation describing a string on an elastic foundation

Homework Statement I'm given an equation describing a string on an elastic foundation: utt+w20u = c2uxx with the boundary conditions u(0,t)=u(l,t)=0. The Attempt at a Solution I think I understand how to do this problem up to a certain point, but that point occurs when I find the...
10. ### LaPlace Equation in Polar

I just got a email telling me I had a response, however I don't see it in the thread. Anyhow, the picture that only shows half the page of paper because that's all the work I had done on it. I got stuck at that point and wasn't sure how to go about calculating the unknown constants (if I had...
11. ### LaPlace Equation in Polar

Homework Statement Solve the Laplace equation: delta u = d2u/dx2+d2u/dy2 inside the half disk 0<r<R, 0<phi<pi Temperature on the bottom side of the disk is zero, u(x,y=0)=0. Temperature on the upper side of the disk is u(r=R, theta) = u0(phi), 0<phi<pi Homework Equations I'm...
12. ### Heat Equation Initial Conditions

Thank you for your help. My teacher had written up our homework in the form that I wrote it in originally, and thus I was having trouble trying to figure out what the initial conditions were exactly. Your post clarified it, and I should be set to solve it now. Thanks
13. ### Heat Equation Initial Conditions

Greetings all, I have a question in regards to my initial conditions. The problem as given is: ut=uxx with u' = 0 at x=0 and u=0 at x=L I was also given u={1 0<x<L/2, 0 L/2<x<L I understand the set up of the problem and the solving of it for the most part, however I'm having...