Recent content by Linday12

1. Question About the Photoelectric Effect for Lower Frequencies

I'm going over the photoelectric effect and have run into a conceptual problem, and was hoping for some help in resolving it. In particular, I am looking at the frequencies below the threshold frequency of whatever metal is being examined. So, because of the lower frequency, there will be no...
2. Coordinates of a particle (coupled differential equations)

Wow, interesting. So \dot{z}=iωz → \dot{z}-iωz=0 because iz=ix-y. Thank you! Sorry, one more question. Now that I have that, when solving it I get z=z_{0}e^{ωt}, but the answer has an additional phase angle \phi in it, so I was just wondering if there was a quick explanation for that. It's...
3. Coordinates of a particle (coupled differential equations)

Yes. I then get \dot{z}=-ωy+iωx=ω(-y+ix). So I can sort of see the relation here now, except my variables seem to be the wrong way, and I have no idea where the \dot{z}-iωz=o comes from still, because i would be gone if the variables were the proper way and I subbed in z for the x-iy.
4. Coordinates of a particle (coupled differential equations)

Hi. I'm not really sure what to do. As far as I know, taking \dot{z}=\dot{x}+i\dot{y}, and \dot{y}=ωx and \dot{x}=-ωy, which doesn't seem to get me anywhere. I have no idea what I am doing.
5. Coordinates of a particle (coupled differential equations)

Homework Statement I'm given two equations for coordinates of a certain particle in the xy plane, \dot{x}+ωy=0 and \dot{y}-ωx=0. Then using the complex variable z=x+iy, find the differential for z, and solve it. Hence give x and y as functions of time. Homework Equations The...
6. Vector Spaces

Homework Statement I'm trying to define a vector space over Q. Does this make any sense? Homework Equations The properties of a vector space The Attempt at a Solution Let V=Q^2 over Q. It seems to me that everything would be defined and I shouldn't be able to do anything to a...
7. Double integral, symmetry

Yes, that is it. I will make sure to do that. Thank you very much!
8. Double integral, symmetry

Homework Statement Let D be the triangular domain given by 0\leq y \leq3, (y/3)-1 \leq 1-(y/3). Then \int\int (e-x^{5}e^(sqrt(1+y^2)) Homework Equations The Attempt at a Solution There is a quick way to solve it by breaking apart the double integral and then, apparently the x^5...
9. Sequences, induction help

Thank you both very much! Those two posts cleared up my problems with it. I was thinking of it in an accumulating way :uhh: (I have no idea why, series and sequence mix up I guess :blushing:), so now it makes sense. :cool: Thanks again!
10. Sequences, induction help

Sorry, I wasn't clear enough. I'm just not seeing how it shows that. I've memorized it and am not really worried about getting it wrong, but it's really not helpful if I don't understand that it keeps under the limit. I guess my induction skills are lacking. Ok, so if ak < 3, then ak+1 =...
11. Sequences, induction help

Homework Statement Let a_n be defined recursively by a_{1}=1, a_{n+1}=sqrt(6+a_{n}) (n=1,2,3,...). Show that lim n->infinity a_{n} exists and find its value The Attempt at a Solution Observe that a_{2}=\sqrt{6+1}=\sqrt{7} > a_{1}. If a_{k+1} > a_{k}, then a_{k+2} = \sqrt{6+a_{k+1}} >...
12. Variation of Parameters, system of equations

Perhaps I'm going about this completely wrong then. How would I start out solving y''+25y=cot(5x). (I should be more specfic, when I say solve, I mean to find A solution, so y_h and y_p. I'm just not sure about how to find the y_p=u1(y_1)+u2(y_2))
13. Variation of Parameters, system of equations

Homework Statement y''+25y=cot(5x) Find one possible solution The Attempt at a Solution I don't have any background in linear algebra, so I can't use cramers rule as a heads up, so I have to solve the system of equations (no linear algebra for this course is needed). Ok, so I take...
14. Undetermined Coefficients, more than one term on RHS

Awesome. That sounds like exactly what I needed to know. Thanks!
15. Undetermined Coefficients, more than one term on RHS

Homework Statement y''-49y=7cos(7x)+7+e^(7x) The Attempt at a Solution I have no idea how to solve this Differential equation. I could solve one that has y''-49y=one term, but I'm stumped with more than one. First, I get the homogeneous equation, y''-49y=0 and fine y_c, then use the...