Modes Definition and 281 Threads

A normal mode of an oscillating system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies. These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge, or molecule, has a set of normal modes and their natural frequencies that depend on its structure, materials and boundary conditions. In music, normal modes of vibrating instruments (strings, air pipes, drums, etc.) are called "harmonics" or "overtones".
The most general motion of a system is a superposition of its normal modes. The modes are normal in the sense that they can move independently, that is to say that an excitation of one mode will never cause motion of a different mode. In mathematical terms, normal modes are orthogonal to each other.

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  1. S

    Normal modes of a two mass, two spring system?

    Homework Statement I have a system of two masses m1 and m2 coupled by two springs with constants k1 and k2. If m1 and m2 are equal what would be the normal modes for this system? Homework Equations Equations of motion for the system: \begin{align*} m_1\ddot{x}_1 &=...
  2. B

    Help with finding normal modes of a bar swinging on a string

    Homework Statement A bar with mass m and length l is attached at one end to a string (also length l) and is swinging back and forth. Find the normal modes of oscillation. Homework Equations L=T-U, and the Lagrange-euler equation, I=(1/12)ml^2The Attempt at a Solution So my idea is this. Use...
  3. dexterdev

    What Are TE/TM Modes in Electromagnetic Waves?

    Hello PF, I have a doubt. polarization refers to the plane of Electric field right?, then linearly polarized wave is TEM and circularly may be TE/TM right? Please someone clear my doubt... What is this TE/TM (m n) modes mean...Any helpful animations other than falstad.com links...
  4. Q

    IR and Raman Spectroscopy With Vibrational Modes

    Homework Statement The question states to identify which graph is associated with which molecule, which are CF4 and CF2Cl2. The graphs are measurements of infrared spectra, one has one peak while the other has two. It then asks to determine which symmetry labels are associated with each peak...
  5. M

    Bell State of two non-orthogonal modes

    Is this possible? If I have, say a photon and two non-orthogonal polarizations \mid0\rangle and \mid1\rangle, can I create a Bell state \mid10\rangle+\mid 01\rangle If not, what is the reason? Thank you :)
  6. S

    Understanding Raman Mode Representation at Specific Wave Numbers

    Why we describe Raman modes At perticular wave number by E1 or A1,A2 or other If E1 say at 645cm-1, Why we cannot describe A1 at this wave number. How we write the representation at perticlar wave number. Please reply.
  7. P

    What Are Residual Modes of Vibration?

    what exactly are residual modes of vibrations? I have come across this terminology in various fem solvers like ansys and pam crash.
  8. reddvoid

    Identifying Wave-guide modes in rectangular wave guides

    How to identify type of wave-guide mode here, like its TE or TM TE01 , TE10, TM11, TE02, TE20 . .. I read number of half wavelengths in x direction is the m and number of half-wavelengths in y direction is n. . .but I can't figure-out how . . .can somebody please explain
  9. U

    Normal Modes - 2 springs question

    Homework Statement Homework Equations The Attempt at a Solution When i do the matrix multiplication of the 2x2 and 2x1 matrix, I get 2 conflicting solutions that don't match at all! So which one do i take to find ratio of X and Y?
  10. brainpushups

    Normal Modes; Rod suspended from strings

    Homework Statement A thin uniform rod of length 2b is suspended by two vertical light strings, both of fixed length l, fasted to the ceiling. Assuming only small displacements from equilibrium, find the Lagrangian of the system and the normal frequencies. Find and describe the normal...
  11. Spinnor

    QED; electrons and photons, different fields, modes of a common field?

    In the Standard Model of particle physics are we to think of the electron(positron) field and the photon field as separate fields? Is it possible to think of the electron(positron) field and the photon field as just different "modes of vibration" of some more basic field? Can this line of...
  12. B

    Small oscillations: How to find normal modes?

    Hi, I'm studying Small Oscillations and I'm having a problem with normal modes. In some texts, there is written that normal modes are the eigenvectors of the matrix $V- \omega^2 V$ where V is the matrix of potential energy and T is the matrix of kinetic energy. Some of them normalize the...
  13. V

    How fast can you 'switch' between superconducting and normal modes?

    The title, basically. If we're at a temperature below the critical temperature (let's just say for a Type 1 superconductor) and an applied magnetic field less than the critical magnetic field, it will be in the superconducting state. But if we increase the field beyond the critical point, it...
  14. retro10x

    Finding Normal Modes (completely stumped)

    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...
  15. G

    Finding Normal Modes of Oscillation with matrix representations

    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...
  16. P

    Density of modes graph from phonon dispersion graph

    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...
  17. J

    First and Second modes of generations and limitation

    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...
  18. Z

    Expanding atomic displacements in terms of all lattice wave modes?

    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...
  19. J

    Physically, what do positive frequency modes represent?

    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?
  20. B

    Wave guide modes: what are they, how are they used

    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...
  21. B

    EM Waveguide Modes: What are they and how are they used

    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...
  22. F

    Modes and numerical aperture of a fiber optic cable

    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...
  23. V

    Chemistry Full Excitation of Molecular Vibration Modes

    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...
  24. Roodles01

    How are modes classified in rectangular waveguides?

    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?
  25. J

    Bloch modes and normal waveguide modes- help to clear up

    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...
  26. C

    Counting electromagnetic modes in a rectangular cavity and boundary conditions

    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)...
  27. S

    Understanding the Different Modes of Potassium-40 Decay

    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...
  28. K

    Why can we see light when looking down a metallic tube? TEM modes can't exist.

    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...
  29. R

    How many modes to include in the modal anlaysis

    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...
  30. O

    String Theory & Particle-Wave Duality: Can Oscillating Strings Explain?

    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...
  31. T

    Normal modes and system's energy

    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.
  32. K

    Analysis of TE and TM Modes: A Closer Look

    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...
  33. N

    IR terms from massless modes in 2D sigma model

    Hi All, My first post here. As far as I've understood there are problems with massless states in two dimensions. In the problem I am working on I have a 2D (non linear) sigma model with a lot of symmetries. The worldsheet fields come as heavy and massless. My main interest is to...
  34. T

    Microcantilever, different resonance modes

    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...
  35. A

    Finding Modes of Vibration in ANSYS

    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...
  36. Y

    Raman spectroscopy-vibrational modes

    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...
  37. A

    Zero-Frequency Modes: Quantum Shape-Phase Transitions in Nuclei

    I'm dealing with the problem of zero frequencies in many body system and it's relation with symmetry breaking. I would like to examine this connection in the case of quantum shape-phase transition in nuclei. I've studied this technique (golstone theorem) in field theory as well as Particle...
  38. fluidistic

    Small oscillations+normal modes of a system

    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...
  39. fluidistic

    Small oscillations+normal modes of a horrible spring system

    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...
  40. S

    Meaning of normal coordinates and normal modes, in relation to phonons

    I am trying to find a succinct definition of normal coordinates and normal modes - relating to numerous coupled harmonic oscillators. What exactly do the normal coordinates describe about these coupled harmonic oscillators? I know that for normal modes, all parts of the system move with...
  41. C

    Exploring Vibration Modes of Cantilever Under Piezoelectric Driving Force

    A computer model has found geometries and frequencies associated with various vibration modes of my cantilever (see pictures). The model only accounts for an anchor at the far end and material properties of each layer. In reality the bottom layer is piezoelectric, it is glued to the glass top...
  42. D

    What Is a Free Mode in an Harmonic Oscillator?

    Hey, I just wanted to clarify the meaning of a "Free Mode" in an harmonic oscillator. From my understanding a free mode is when the system is in motion, so for example if there were a loop, with a spring around it and two masses attached to the spring, the first mode is a free mode, when...
  43. U

    Understanding Vibrations: Natural Modes and Frequencies

    Hi, I'm trying to understand vibrations and specifically what happens in the natural modes of frequency.. 1. It seems that the harmonic nature of solution(with Acos(wt)...where A is the amplitude) applies only in the natural mode of vibration...and so the system will have a defined mode...
  44. N

    Longitudinal modes in a fibre laser

    Hi In the Wiki article on longitudinal modes (http://en.wikipedia.org/wiki/Longitudinal_mode) they state that: "The analysis of longitudinal modes is especially important in lasers with single transversal mode, for example, in single-mode fiber lasers. The number of longitudinal modes of such...
  45. M

    What is the difference between normal modes and propagation modes?

    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.
  46. T

    Constant in Modes of Optical Fiber

    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...
  47. V

    Finding the Normal Modes of a 3 mass molecule connected by springs

    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...
  48. T

    Normal frequencies and normal modes of a multi-part system

    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...
  49. M

    Normal Modes Solution for Two-Body Oscillator

    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...
  50. K

    What are the differences between token ring modes in a token ring LAN?

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