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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...

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...

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.

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.

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...

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...

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

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...

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!

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 =...

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}} >...

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))

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...

Awesome. That sounds like exactly what I needed to know. Thanks!

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...

Thank you, that was exactly what I needed!

Homework Statement \frac{dy}{dx} = \frac{3xy}{3x^2+7y^2}, y(1)=1 Express it in the form F(x,y)=0 The Attempt at a Solution I'm not sure where I'm going wrong. I let v=y/x, v+x\frac{dv}{dx} = \frac{3x^2v}{3x^2+7x^2v^2}=\frac{x^2(3v)}{x^2(3+7v^2)}= \frac{3v}{3+7v^2} \Rightarrow...

Ok, thanks. I'm still unsure if I did the question properly. I know the answer is right, but I'm just not sure whether the work is right or not.

Sorry, I couldn't get the script right. Its \int \frac{dx}{\sqrt[3]{x^2 - 7}} from 8 to infinity

Homework Statement Determine if the following is improper and convergent, improper and divergent, or proper \int \frac{dx}{\sqrt[3]{x^2 - 7}} from 8 to infinity The Attempt at a Solution Since I don't know how to...

Homework Statement I'm confused about integrating something like \int\frac{1}{u} Sometimes the answer seems to be ln|u| and sometimes just ln(u), and I wasn't sure why it is different from problem to problem. (after subbing u back in; I'm using the u-sub method) It looks like the answer should...

Ok, so \frac{ds}{dh} = \frac{10}{4-h} + \frac{10h}{(4-h)^2}, when the height, h, is 3, is equal to 40. So, then \frac{dh}{dt} * 40, and solving the dh/dt for 1m/hr, makes the shadow have an increase of 40 m/hr at h=3. Hopefully I'm starting to get it.

Hmm, I am stumped. I'm not seeing how to do it at all.

Sorry, I'm not quite sure what I'm doing. I got the 3 for the height from the question, asking the shadows rate of increase at 3. It's a one variable calculus course, so I was avoiding t to keep it down to one variable, I'm not sure at all how to do differentiation with two variables. I could...

Interesting. So, \frac{ds}{dh} = \frac{10}{4-h} + \frac{10h}{(4-h)^2} where h is 3, the shadows rate is increasing at 40... metres every 3 hours? That has to be wrong, since it doesn't really make any sense to me. I'm unsure of what the units would be. And, when it approaches 4, the...

I think I understand what you mean (for a single variable course). And if I have 3 variables, that is one too many. So, since h is variable, then 1 must be variable t, and I can state it as 4-h. So, \frac{4-h}{10} = \frac{h}{s}, so s=\frac{10h}{4-h}, and s'(h)=\frac{10}{4-h} +...

Ok, so taking that into account, I have \frac{1}{10} = \frac{h}{s}, which then can be solved to become s=10h. s'=10, so the rate at which the length s is increasing is 10 metres per hour. I'm still not sure where the stalk growth of 1 metre per hour comes in at then.

Thanks, I'm studying for a final, and on the finals from prior years there seems to be questions like this one asked. So, after drawing the other line, I can see two triangles in the diagram. I know the details of the one triangle, so if I remember correctly, I can find the details of the other...

Homework Statement A magic stalk starts growing at a spot 10 metres from a 4 metre lamppost. The stalk grows 1 metre per hour. Find the rate at which the length 's' of the stalk's shadow is increasing at the instant when the height h of the stalk is 3 metres. The Attempt at a Solution...

Interesting. Let me see if I understand. x(y)-2y=1-2x <----Am I to factor(not sure if that's the proper word) the left side to get that final answer then, similar to what you showed? And then I get y(x-2) after the factor Which then is y(x-2)=1-2x And then I can get my final answer of...

Homework Statement If f(x)=\frac{2x+1}{x+2}, the equation for y=f^-1(x) is? So I switch x, x=\frac{2y+1}{y+2} The Attempt at a Solution I've tried many ways, but I must be going wrong somewhere, here's what I think to be my nearest: x(y+2)=2y+1 x(y)+2x=2y+1 x(y)+2x-2x=2y+1-2x...

If your still on this question: You could actually use two approaches to calculate the electric field, you've given the equations. You might want to go over your notes a little more to gain some insight and, the potential difference looks right, but as for the negative, I'm not quite sure...

Homework Statement I have two graphs (Radiant Power vs wavelength) and I have to choose which one would be the best for a shop -- the one with the least yellowing. (fluorescent bulbs) I wasn't sure how to tell. The emission spectrums are very similar. The continuous spectrums are different...

Homework Statement A photon enters an atom in the ground state. I have the energies to get to the next level. My question is, does the photon have to be the exact energy to get to the next level before it is absorbed, or can the atom absorb it and go up those few levels and.. sort of store the...

It's late and I'm not sure if I'm looking at this properly, but I would just like to say to take another look at the equations for your electric field calculations. There are two different charges in the problem, so be careful distinguishing which one is the "test charge" and which one is...

Wow, I can't believe I didn't notice that I hadn't used the plate separation. The problem makes complete sense now. Thank you both for your help, it was exactly what I needed!

Homework Statement In an experiment similar to J. J. Thomson's, charged particles are observed to travel through a magnetic field of 0.040 T with a radius of curvature of 0.20 m. The path of these particles is made straight again when an electric field is introduced by two parallel plates...

Homework Statement I'm doing an assignment involving a current balance, and the one thing I don't understand is the currents. I have two separate currents, one labeled "Current in Solenoid" and another labeled "Current in Loop". Now, I know the current in the loop is the part that causes...

That's what I initially had, but I always want to read too much into it lol. Thanks for the clarification!

[SOLVED] Wording Question Regarding Angles If it says "to the horizontal", such as 30 degrees to the horizontal, would the angle be measured from Y or X? I measured it from the horizontal, but reading it over, it sounds like it's measured towards the horizontal, so I was thinking it may be from...

Thanks.

[SOLVED] Force Calculations If an object is being pushed horizontally, does Fnormal always equal Fg? And Ffriction only equals Fapplied if it's at a constant velocity? I think that's how it goes, but I'm a little unsure. Thanks!

Yeah. Thanks a lot, I'll make sure to do that.

[SOLVED] Significant Digits I know how to do significant digits, but was wondering about answers involving multiple equations. If I find acceleration first, then find net force, should I wait to round the answer until the end? a=vf-vi/t and then fnet=ma To reiterate, should I keep...

Thank you very much!

[SOLVED] Question On Displacement -- Velocity-Time Graph When calculating displacement, if you have a graph that starts with a non zero velocity, do you calculate the area from zero still, or do you calculate only from where it starts? For instance, a linear problem with a velocity starting...

Ok. They were released simultaneously, so now I've got to figure out if it's an error in the diagram. Thanks.

[SOLVED] Independence of Motion I have a problem with a diagram that goes along with independence of motion. When air resistance is negligible, objects are supposed to fall at the same rate. In the diagram (a flash photograph), it shows 2 balls falling, one straight down, and the other...

Thank you. That was exactly what I was lost on!

Ok, The velocity-time graph in this case is simpler, and is a series of straight lines (not curved). So, I wouldn't have to draw the tangent, would I? Do I have to pick another point on the line and use it? How would this give the acceleration for the given point, and not for a time interval...