# Search results

1. ### Diffusion Problem (Conduction)

Thank you for trying to help me. I have tried a lil bit but I got confused so I guess I wanna make sure that what I am doing is correct. X(x)=A*cos(lambda*x)+B*sin(lambda*x) X(x=0)=A*cos(0)+B*sin(0)=>A=0 X(x=2)=0=>B*sin(2*lambda)=0 Lambda=((n*Pi)/L)^2 so the eigenfunction EF...
2. ### Solve y''+9y=delta(t-pi)

Yes now I understand what you mean. The answer to this problem is thus a/b=-1/2 :) This problem is now officially solved :D Defennder, thank you so much for your help. I learned alot!
3. ### Solve y''+9y=delta(t-pi)

Thanks for all the help. I would say u(t-pi) goes to zero? So I will be left with y=1/3sin(t)+cos(3t) ... I cant get an exact fraction I get this to 1.05...how do you get exact fractions?
4. ### Solve y''+9y=delta(t-pi)

So then my u(t-a)f(t) is equal to f(t) as Pi is smaller than (14*Pi)/9. Now I will only have: t=((14*pi)/9)=4.886921906 into cos(3t) & 1/3sin(3t)... cos(3t)=-0.5 1/3sin(3t)=-0.32827 f(t-a)=1.745329 y=1.745329-0.5-0.32827=0.917059 Is this correct?
5. ### Solve y''+9y=delta(t-pi)

Ok I have read your message 20 times now...and I'm still confused. I follow until the fact that f(t-a) is the inverse Laplace transform of 1/(s^2+9) shifted by -a. So then f(t-a)=1/3sin(3(t-a))u(t-a)? Is a=pi? How do I get the fraction a/b out of all this? I'm gonna plug in some numerics and see...
6. ### Solve y''+9y=delta(t-pi)

Can't anyone shed more light on this problem?
7. ### Solve y''+9y=delta(t-pi)

I plugged in t=((14*pi)/9) into cos(3t) & 1/3sin(3t)... cos(3t)=-0.5 1/3sin(3t)=-0.32827 I still don't know what to to about the heaviside-term. How can I evaluate that numerically? And how do I get a fraction a/b from all this? Any ideas or suggestions?
8. ### Calculus question

You did the same mistake I did when I started asking questions here and initially didn't show my attempt for a solution. As I did notice it myself later on...it actually helps if you show at least one of your attempts - even for self-reflection about the problem. Have you tried to cross-multiply?
9. ### Solve y''+9y=delta(t-pi)

I see...is this what you mean? u(t-a)f(t-a)*(1/3)*sin(3t-a) Is the a-value for the shift pi? If this is true, will this be the expression for y: y=u(t-pi)f(t-pi)1/3sin(3t-pi)+1/3sin(3t)+cos(3t) How will I evaluate the first term in the expression above numerically?
10. ### Solve y''+9y=delta(t-pi)

After some thinking about the Heaviside term I came to the conclusion that the last term in the attachment above should have an inverse Laplace transform of: u(t)f(t-pi)*(1/3)*sin(3t) If this is correct (please object if it is not) as I add all three terms I should get...
11. ### Solve y''+9y=delta(t-pi)

I have the following... http://img71.imageshack.us/img71/4016/mathprob1na5.jpg" [Broken] But I'm not sure about that Heaviside function term. I really don't know what to do with (s^2+9) in denominator? Isn't there a jump (discontinuity in Heaviside functions)? I have not y yet. If I add these...
12. ### Solve y''+9y=delta(t-pi)

Oh yeah and Laplace Transform of f(t-a)u(t-a) is exp(-a*s)F(s) is that correct now?
13. ### Solve y''+9y=delta(t-pi)

The Laplace Transform of cos(at) is s/(s^2+a^2) The Laplace Transform of sin(at) is a/(s^2+a^2) and Laplace Transform of f(t-a)u(t-a) is exp(-Ts)F(s) Now I will try to inverse-transform them individually.
14. ### Solve y''+9y=delta(t-pi)

Thanks for letting me know...I hope this works:) http://img57.imageshack.us/my.php?image=mathprobkv7.jpg"
15. ### Solve y''+9y=delta(t-pi)

I just don't understand how these three fractions can give me y at the end. Is the approach of inverse transform incorrect? Cause, just by looking at s/(s^2+9) I can transform that to cos(3t) but what do I do with the rest. How can these three "add up" to give me the fraction a/b?
16. ### Solve y''+9y=delta(t-pi)

Defennder thanks for pointing that out. So now I have the following:
17. ### Solve y''+9y=delta(t-pi)

I can't figure out how to get the inverse transforms...any ideas?
18. ### Diffusion Problem (Conduction)

Can anyone help me with this problem please? I'm stuck...
19. ### Solve y''+9y=delta(t-pi)

I am now at the stage where I need to get the inverse transforms but I don't remember how...
20. ### Solve y''+9y=delta(t-pi)

Solve the differential equation y''+9y=delta(t-pi) that fulfills the initial condition y(0)=y(0)=1. Answer by giving the value for y((14*pi)/9). The answer can be given by a fraction a/b. The Attempt at a Solution I will submit my attempt for a solution as an attachment shortly.
21. ### Diffusion Problem (Conduction)

I know that I need to consider temporal and special separately. For the spatial do I have to consider Lambda=0, Lambda<0. Lambda>0 cases?
22. ### Diffusion Problem (Conduction)

T(t)= Ce^{-\lambda^2 t}. Now you can use the boundary conditions, that u(0)= 0 and u(2)= 0, which tell you that X(0)= 0 and X(2)= 0, to determine what values \lambda can have (so that sin(2\lambda)= 0) as well as the fact that the coefficients of cos(\lamda x) are all 0 (so that X(0)= 0)...
23. ### How to impress prof in research

Yeah me too. But once he started cursing it was not pleasant anymore. If you are gonna publish something in your own name I believe that if you see an obvious mistake you must share it with your professor. Especially if the mistake is trigged by him in your research. I believe in mutual respect...
24. ### How to impress prof in research

Yeah, I was reading about your pieces of advice and i must say that sometimes keeping a low profile helps. I say that from experience(I have two Master's degrees (One in Aero and one in Mech Eng). I had a scientific argument with my professor one day and it led to the fact that I had to leave...
25. ### Diffusion Problem (Conduction)

I will post my initial approach as an attachment. Do I apply the boundary conditions while I have solved for u?
26. ### Diffusion Problem (Conduction)

Homework Statement Since the problem involved formulas I have posted it as an attachment. Please check the attachment first. (I have not scanned this problem, just wrote it in word and posted it) The Attempt at a Solution My approach on this problem is to start with separation of variables...
27. ### Fourierseries of X^2-1

Nick...thanks so much. What you said made perfect sense. I was disregarding the terms for n=3 and that's what I did wrong. So, now my answer is correct; a=-4 and b=9. Thus, This problem is solved:)