Modes Definition and 243 Threads

Homework Statement Two horizontal frictionless rails make an angle θ with each other. Each rail has a bead of mass m on it and the beads are connected by a spring with spring constant k and relaxed length=zero.Assume that one of the rails is positioned a tiny distance above the other so that...

Homework Statement Two equal masses (m) are constrained to move without friction, one on the positive x-axis and one on the positive y axis. They are attached to two identical springs (force constant k) whose other ends are attached to the origin. In addition, the two masses are connected to...

While practicing for an upcoming exam, i ran into this question that has truly got me stumped. A phonon dispersion graph is given for NiAl (attached), and then they ask you to schematicaly plot the density of modes graph. I have the result of what is should look like, but i do not understand how...

In Joseph Dauben's book on George Cantor, his philosophy of the infinite and hsi mathematics...there is a section which talks of the first mode of generation, the second mode of generation and the principle of limitation. Any words, any of you would like to use to describe all three of...

I find the expression: "In general, one can expand the atomic displacements in terms of all the lattice wave modes (resembles a Fourier series expansion)" at: https://courses.cit.cornell.edu/ece407/Lectures/handout17.pdf But I have not found the expression in any other literature. (In fact...

I know this is a basic question, but why are positive frequency modes so important when expanding a field operator. Furthermore, what do they represent?

I posted this in the EE forum but I think the physics forum may be more helpful. Title pretty much says it all. In EM waveguides (rectangular, circular, what have you), I understand there are various "modes." I'm trying to get a better physical understanding of all the various parameters and...

Title pretty much says it all. In EM waveguides (rectangular, circular, what have you), I understand there are various "modes." I'm gathering that these represent specific, discrete solutions to the Hemholtz equation, and therefore there are only specific frequencies that will propagate? What...

Hello Forum, the numerical aperture NA of a fiber optics is given by the square root of the squared core index minus the squared cladding index. The NA indicates the angular ability to collect light from the outside of the fiber, i.e. the max semi-angle over which light will enter the fiber...

Homework Statement Given the relationship Cp/R as a function of Temperature, approximate the number of fully excited vibration modes at a given temperature for a given molecule. 2. The attempt at a solution I have looked through several textbooks and many web sites, but I can't find this...

Homework Statement How do I classify modes? If there is a rectangular waveguide how can I show it is operating in TE10, TE20 or TE11 mode. Homework Equations Could someone help clarify how the 10, 11 or 20 comes about? Is it due to the dimensions of the guide or something else?

Hi all, I'm a little confused about Bloch modes vs. waveguide modes of a single waveguide and was wanting some pointers. I read that Bloch modes are results of the wavefunction of a particle (usually, an electron) placed in a periodic potential. In the case where we have an array of cylinder...

The electric field in a cubical cavity of side length L with perfectly conducting walls is E_x = E_1 cos(n_1 x \pi/L) sin(n_2 y \pi/L) sin(n_3 z \pi/L) sin(\omega t) E_y = E_2 sin(n_1 x \pi/L) cos(n_2 y \pi/L) sin(n_3 z \pi/L) sin(\omega t) E_z = E_3 sin(n_1 x \pi/L) sin(n_2 y \pi/L)...

1)Is Potassium-40 dangerous material?How dangerous is it?Does it belong to restricted materials? 2)Why Potassium-40 decays in such different modes such as beta decay,electron capture, and positron decay?What could be done to prevent it decay in other ways with exept beta decay?Or what could be...

Hey everyone, I'm going over my course content for an exam this Saturday and I'm a bit confused by a realisation I've just had. In a metallic waveguide we know there are no TEM modes. But wouldn't this mean that we couldn't see through metallic waveguides as we see electromagnetic radiation...

hi all, Having those input in hand, mass ([M]) n*n matrix , stiffness ([K]) n*n matrices and having obtained the eigen-values, eigenvectors for the higher-frequencies with subspace or simlutaneous iteration respectively, eigen-values ([\Phi]) as m*m diagonal matrix, and m*m eigen-vectors as...

I'm not sure if this question is something that has been asked before or if i thought about it myself or if it's completely ridiculous! But I was thinking, if, according to String Theory, particles are 1-dimensional strings that go through modes of oscillation, could they describe how a...

Hi, why does the energy of the system equals the sum of the energy of the modes? The book I'm reading only states it, it doesn't prove it.

I'm a little confused about the analysis of TM and TE modes. As per definition, TE modes have only H (magnetic field) in the direction of propagation and TM mode has only E in the direction of propagation. But we also know that when an electromagnetic wave propagates in a medium, E and...

I'm now styduing micro-cantilever used as a sensor. It is usually made of silicon based materials. In a certain condition below, the cantilever will vibrate itself when a certain external frequency is applied. <condition> Certain cantilevers may exhibit mode coupling depending on...

Hi, I'm playing around with ANSYS to find the modes of vibration of a structure. How do I know which are the most important modes? I understand that there are infinite modes of vibration - getting higher and higher in frequency. I'm guessing that it has something to do with the effective...

Hi everybody, I am trying to learn how I can interpret the Raman spectra. How can we know which peak corresponds to which vibrational mode? We can find it by doing a simple literature scan that's ok but without literature scan, how can we know it? Is there any software? I did a basic...

Homework Statement Two identical pendulums of length l hang from a ceiling. Their vertical axis is separated by a distance l_0. They are made by 2 masses m. Between these 2 masses we put a spring of constant k and natural length l_0. Gravity acts verticaly downward. 1)Calculate the proper...

Small oscillations+normal modes of a "horrible spring system" Homework Statement Let 2 particles of mass m be like in the attached figure. All springs have a constant k and natural length l_0. The particles are only free to move horizontally. Calculate the characteristic frequencies of...

What is the difference between normal modes and propagation modes? I am confused. I know that normal modes are natural modes of vibration of a system. And, propagating modes are ... ? Thanks.

Dear All, Many thanks for reading this query. Actually, I am having problem in measuring the mode fields of Optical fiber at the core-cladding interface analytically for modes LP01 and LP11. The modes are normally given by eq 2.165 (image attached). To my knowledge these constants A and C...

Homework Statement Hi everyone! I'm trying to solve a problem involving 3 equal masses (m) arranged in a 45-45-90 right triangle, each mass connected to the other two by a spring, and all the springs have the same spring constant (k). So it should look like this: Where I have made a...

Homework Statement ***This is problem 11.29 in Taylor's Classical Mechanics*** A thin rod of length 2b and mass m is suspended by its two ends with two identical vertical springs (force constant k) that are attached to the horizontal ceiling. Assuming that the whole system is constrained to...

Hello! For a coupled two-body oscillator we write the general solution as: x1(t)=C1-Cos[ω-t+ψ1-]+C1+Cos[ω+t+ψ1+] x2(t)=C2-Cos[ω-t+ψ2-]+C2+Cos[ω+t+ψ2+] Where we determine C1-/C2- and C1+/C2+ from the normal mode condition. We call ψ1-=ψ2-=ψ- and ψ1+= ψ2+=ψ+, and we end up with 4...

In a token ring LAN (IEEE 802.5) what are the differences between "Single token", "Multiple token" e "Single packet"? Thanks in advance.

Homework Statement I'm stuck at understanding how to find the kinetic and potential energy matrices such that the determinant |V- \omega ^2 T|=0 when solved for \omega, gives the normal modes (characteristic frequencies?) of the considered system. For example in Goldstein's book for a molecule...

Most texts on radioactivity starts by saying "there are three important modes of radioactivity-alpha, beta and gamma..." and goes on to describe their properties. But why are there only a few modes of radioactivity? Does that mean the modes observed so far, or, are there theories to describe the...

Hi. How can i find out the temperature rise in a steel plate of known dimensions, when exposed to sunlight, losing heat to air flowing over it by convection, and heat getting transferred to another body by convection? I hope to hear about the different approaches that could be taken. Thanks...

Homework Statement 1. A double pendulum, consisting of a pair, each of mass m and length l, is released from rest with the pendulums displaced but in a straight line. Find the displacements of the pendulums as functions of time. === So... this is a problem from Kibble's Classical Mechanics...

Homework Statement The first part of the problem is just finding the Lagrangian for a system with 2 d.o.f. and using small angle approximations to get the Lagrangian in canonical/quadratic form, not a problem. I am given numerical values for mass, spring constants, etc. and am told to find the...

I'm having trouble understanding why only certain angles of propagation can transmit down an optical fibre. My lecturer produces this formula for the allowed angles: \sin \theta = p \frac{\lambda}{2dn} where \theta is the angle of the ray from the optical axis \lambda the wavelength of light d...

Hi, everyone. I'm required to complete an open ended analysis of the following problem: http://imagefrog.net/show.php/146581_image.png http://imagefrog.net/show.php/146581_image.png I'm not requesting a solution, I'm only looking for assistance in relation to determining the spring stiffness...

Homework Statement Two equal masses are held on a frictionless track by 3 equal springs, attached to two rigid posts. If either of the masses is clamped, the period (t=2pi/w) of one oscillation is three seconds. If both masses are free, what is the periods of oscillation of both normal...

So I have a spring problem where I have two masses and three springs hanging down from a ceiling. Each spring has a different force constant and each mass has a different weight. |.....| |Spring 1...|Spring 3 Mass 1...|...

Homework Statement Please see question attached Homework Equations The Attempt at a Solution Ok so I've been able to do the first few parts and have derived that Wm,n = c pi / L (m^2 + n^2) I've thus been able to show that the second lowest freq is a factor of root(5/2)...

Dear Friends, I am new to this forum and I am not sure whether I am writing my Query in the correct section or not...If not Kindly guide me where to post this... I am confused about what are normal modes of propagation in isotropic or anisotropic media?? or How one can define Normal modes...

Have a project to do on an acoustic resonance chamber, a loudspeaker attached to a perspex box with a copper pipe, there was a microppohne inside the chamber connected to oscillloscope. We investigating a few variables in most detail was route [1] [1]damping by chainging materials in the...

Homework Statement In textbooks, I often see the sum of the first two normal modes given in the equation attached (on the right). I'm wondering how they arrive at that equation based on the general formula (on the left). I tried subbing in n= 1 and 2 in the general formula, but I'm not sure...

Homework Statement The first circuit has a capacitor with capacitance c and an inductor with inductance L. In series with this is another capacitor which is connected to the next loop in the circuit. It look something like http://imgur.com/YJDaD.png" Sorry for the crude drawing...

I did this in ANSYS, but I am wondering what is the analytical solution to this. Does anyone know?

The question is more of a mathematical question then one about physics in the attached file between equations 6 and 7 it says "integration over the modes" i don't know how they go from the integration measure \int D\phi \rightarrow \int D\phi_1 D\phi_2...D\phi_N any advice would be...

Hello all, what is meant by soft optical modes. Is it just the Einstein modes with low frequency ? thanks.

Hello chemists, One help..I read in some articles about Fe-H and Fe-D modes.. For eg., FeH6 means One Fe bonded to 6 H atoms... But in Fe-D...'D' means what? thanks

there are three molecules joined through three springs of equal length 'l' forming an equilateral triangle , if all three molecules are displaced by equal lengths, they start oscillating linearly. write the simulation for both, the original problem and the linear one.

Like phonons? Even if SF is a random lattice, there might be modes emerging from some space of phase space. Look at this example from BEC quantum Chaos: http://www.theo-phys.uni-essen.de/tp/forsch/bec.html