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Ok, let's see, N will be zero when gravity loses it's effect on the sand, which means, when velocity of the sand (along with the membrane) is such, that it's acceleration is equal to gravity acceleration, just with opposite direction. Is that right?

So when ##a_m-g<0## they diverge, since ##a_m=-Aω^2sinωt## it means that ##-Aω^2sinωt<g## but what i am supposed to do next, we will have maximum velocity at equilibrium point, since after reaching equilibrium point it begins slowing down, right? Now, i should, as you said, use maximum velocity...

Maybe when they reach equilibrium point, but i am not sure, could you explain it to me?

Oh, that's what you meant, i didn't knew it's called vertical displacement function, i always refer to it as elongation in function of time, anyway, what's with the starting phase, is it zero or what?

I am sorry but i don't know how to transfer frequency into vertical displacement function. Can you help me with that?

Homework Statement A little amount of sand is spilt over horizontal membrane that oscillates with frequency f=500Hz in vertical plane. If sand grains are jumping to the height h=3mm with respect to the equilibrium position, find amplitude of oscillation of membrane. Homework Equations ω=2πf...

Ok, let's see if i understand this now. This is the same image i posted before, it just has that one angle labeled. If force that is straining this wire is F and it is acting both from the left and right part of wire, then the net force that is acting is sum of those two forces along the...

I don't understand you very well, why is restoring force (if by restoring force you mean the force that tries to return wire to original position) is twice the component of the tension in the wire?

This is all i have, i don't know how to draw force F, force F1 is the force that pulls the pellet out of equilibrium position. How can i draw the force that strains wire?

Homework Statement There's a horizontal thin wire whose mass is negligible and whose length is l=1m. It is strained with constant force F=10N. If we place a tiny pellet in the middle of wire (mass of pellet is m=1g) and then we bring wire out of equilibrium position (moving out of it's original...

That's exactly what i thought, it might be that they meant a torque on the magnetic moment, but i wasn't completely sure. Anyway, i needed approval that i can't determine m by using the fact that i know B, i mean, that there's no formula that is used to determine m by knowing B.

Homework Statement If there's a current I flowing through the rectangular conductor and it's located in the magnetic field in such way that normal vector of the surface that this rectangle forms closes the angle of 60 degrees with magnetic induction vector find total magnetic moment of this...

Thank you for your help. I'll check out that "Insight" paper of yours.

I've tried to find that more basic definition of k in my books and notes, but i couldn't, but i found something that can be related to this problem, i found out that if whole flux through first coil goes through second coil (through it's cross section to be precise) that then we have perfect...

But there are magnetic surface currents here, right? What about them?

flux in the first coil is ##Ф_1=N_1L_1I_1## and flux in second coil is ##Ф_2=N_2L_{12}I_1## but how can i represent k in terms of these values?

There's no any other requirements, it just says to find k.

No, there's no special requirements, it only says that i should determine k.

Thank you a lot, I've been struggling with this for a while (now it seems relatively simple, but it wasn't at the beginning though), but i think that i understand this now, anyway, thanks again!

Homework Statement Two coils of wire that have same shape and dimensions are thickly rolled up so that the coincide, they only differ in number of coils (windings) N1 for the firs one and N2 for the second one (N1<N2). When there's constant current in the first one and there's no current in the...

Again, sorry it took me so long to respond. I tried to find vector B using Ampere's law and this is it: That little contour i drew is the contour on which i will implement Ampere's law, anyway, the general for of Ampere's law is: ## \int \vec H \vec dl = I_{through C} ## C is contour ##...

Thanks again, i see now, i thought that it was the same formula as mine, but there's a dot product in yours, now that method isn't familiar to me, so it would be better if i use another method, like Ampere's law, i will try to solve it that way and then i will post my work here.

Thank you very much for your answer, i am really sorry it took me so long to respond, but i appreciate your effort to help me on this one, since it was somehow confusing for me. Anyway, only idea i thought of was the first idea you mentioned, but, as you stated, it is mathematically difficult...

I understand what are you saying, it's because of the cross product. Thanks a lot for help!

Homework Statement We have a very long ferromagnetic cylinder with square cross section, with side length a. Cylinder is homogeneosly magnetized over his volume so that the magnetization vector is parallel to the axis of cylinder. Cylinder is in vacuum. Find the current appeared in the cylinder...

Finally someone responded! :) Ok, i know, B is a vector too, but if we look only at intensity, is my final solution in my previous post correct?

Homework Statement We have contours C1 and C2 located in vacuum and there are constant currents in them, I1 and I2 respectively. Find the expression for magnetic force that acts on one very small element (dl) of the circle C2 and it's coming from one very small element of the contour C1...

1. The problem statement, all variables and given/known data We have a superconductive contour in the shape of circle with radius ##a##. Inductance of contour is ##L##, when the contour is out of magnetic field, there's no current in it. What's the current in the contour when constant magnetic...

I think i understand that part now. After this i actually need to calculate the energy in the core using the diagram, i will try that it should work. Thanks.

I don't quite understand this, does it means that i can use 1\2BH or not? What happens to the Wm(magnetic energy)? About that triangle you mentioned, i don't see any triangles when H is from 0 to 2000, i can see it when H goes from 0 to 500. But, how can i determine the value of H for which I'm...

What is dWm equal to then? is it: ## dW_m = \frac{1}{2}BHS(l_1 + l_2) + B_0H_0Sdx ## ?

It's just a mistake in the text of the example, but i wanted it to remain the as it is, maybe it makes no sense, but it won't affect the procedure of solving. Why i can't? I mean the only thing that affects the change of energy is change of volume of fissure. Which means that i don't need H or...

Homework Statement If we have a system that is shown in the picture, the upper piece is magnet, and if we know the following data: S = 1cm2 which is area of material, S0 = 1.2cm2 which is the area of fissure. To bring these tow pieces of this system magnetic induction in the fissure should be...

Matrix diagonalization? I know that if i have upper or lower triangular matrix that determinant of such matrix is product of elements on the diagonal, if that's what you meant.

Well, i think i understand the idea, but the fact that sings are switching is confusing me, i mean, when i have something like this: ## \sum\limits_{k=1}^n \frac{1}{2k}## (which is almost exactly the same as in this case, except for the (-1)k part) then it's simple: ## \sum\limits_{k=1}^{n-1}...

Homework Statement If we have a number sequence such that: a0, a1 are given, and every other element is given as ##a_n=\frac{(a_{n-1} + a_{n-2})}{2} then express an in terms of a0, a1 and n , and fin the limit of an Homework Equations The Attempt at a Solution If i try to express a3 in terms...

I don't understand what you mean, could you explain me this part?

Homework Statement I have to solve the following determinant ## D_n=\begin{vmatrix} 1 & 1 & 1 & \cdots & 1 & 1 & 1 \\ 1 & 1 & 1 & \cdots & 1 & 2 & 1 \\ 1 & 1 & 1 & \cdots & 2 & 1 & 1 \\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots \\ 1 & 2 & 1 & \cdots & 1 & 1 & 1 \\ 1 & 1 & 1 &...

I think i solved it, lowest r = 20 so ## \phi = \arcsin\frac{4}{5}##. But, i would really like if you could explain me geometrical approach (i hope I am not bothering you too much), it might help me understand what is really going on there.

But, how can i find the lowest possible value, is it by taking derivative?

Ok, let's see, ## r^2cos^2\phi + (rsin\phi - 25)^2 \leq 225 \\ r^2cos^2\phi + r^2sin^2\phi - 50rsin\phi + 625 \leq 225 \\ r^2 -r50sin\phi +400 \leq 0 ## So i ended up with quadratic equation by unknown r, but i don't know ##\phi## either.

Homework Statement Of all complex numbers that fit requirement: ## |z-25i| \leq 15## find the one with the lowest argument. Homework Equations The Attempt at a Solution z=a + ib (a, b are real numbers) ## \sqrt{a^2 + (b-25)^2} \leq 15 \\ a^2 + (b-25)^2 \leq 225 ## The lowest possible...

Well, if it's complex number, i can do that by multiplying with it's conjugate, that's what i did, i can't remember something else.

Let's see, i guess i could multiply numerator and denominator by ## cos\frac{2k\pi}{n} + 1 - sin\frac{2k\pi}{n} ## is this the thing i should do?

I think i know what are you trying to say, denominator can't be zero, so this works for every k and n except when n=2k.

Well, i think it could go this way: ## 1+a=k-ka \\ a+ka=k-1 \\ a=\frac{k-1}{k+1} \\ a=\frac{e^{i\frac{2k\pi}{n}}-1}{e^{i\frac{2k\pi}{n}}+1} ## Is this correct?

Ok, so, i have ##\frac{1+a}{1-a}=e^{i\frac{2k\pi}{n}}## , but i should find a, what should i do next? Since a is complex number a=x +iy (x, y are real numbers) and then if i multiply and divide LHS by by 1-x +iy it doesn't seem like it gets me any closer to the solution.

Well, there are n solutions to such equation, ##z=cos\frac{2\pi +2k\pi}{n} + isin\frac{2\pi +2k\pi}{n}##

Homework Statement Solve the following equation: ## (1+a)^n=(1-a)^n## where a is complex number and n is natural number Homework Equations Euler's formula The Attempt at a Solution I've tried something like this ## (1+a)^n=(1-a)^n \\ (\frac{1+a}{1-a})^n=1 ## But i really have no idea...

Let's see: I have ## P_n(-1) = (-1)^n + a_{n-1}(-1)^{n-1} + \cdots + a_1(-1) + a_0## and ## P_n(-1) =(-1-\alpha_1) \cdots(-1-\alpha_n)## Now, taking all -1's out i have ##P_n(-1) =(-1)^n(\alpha_1+1) \cdots(\alpha_n+1) = (-1)^n + a_{n-1}(-1)^{n-1} + \cdots + a_1(-1) + a_0## Multiplying both...