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. bananabandana

    I Negative and Positive energy modes of KG equation

    If we have the normal KG scalar field expansion: $$ \hat{\phi}(x^{\mu}) = \int \frac{d^{3}p}{(2\pi)^{3}\omega(\mathbf{p})} \big( \hat{a}(p)e^{-ip_{\mu}x^{\mu}}+\hat{a}^{\dagger}(p)e^{ip_{\mu}x^{\mu}} \big) $$ With ## \omega(\mathbf{p}) = \sqrt{|\mathbf{p}^{2}|+m^{2}}## Then why do we associate...
  2. Feodalherren

    First natural frequency for bending, axial and torsion modes

    Homework Statement We have a rod of length L fixed to a rigid support. At the end of the rod there is a mass, m. Assume that the rod has no mass. Find the first natural frequency for the bending, axial and torsion modes. Homework EquationsThe Attempt at a Solution So I'm reviewing some stuff...
  3. S

    Why are we only considering the first eigenfrequencies?

    Hey, I have a question concerning eigenfrequencies: Let us assume we examine a beam that is fixed at one end and free at the other end. It is possible to get an analytical solution in form of a unlimtied series: sum_i=1..infinity eigenfunction(i)*exp(i*eigenfrequencie(i)*t). (something...
  4. R

    Modes of Vibration of 3-DOF Spring Mass System

    Homework Statement Homework Equations a11 = a21 = a31 = a12 = a13 a22 = a32 = a23 $$ \begin{bmatrix} x_{1} \\ x_{2} \\ x_{3} \end{bmatrix} =ω^2m \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}...
  5. U

    Laser Question - Axial Modes & Gain Saturation

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  6. S

    I Detectable interference between counter-propagating modes

    Is it possible (in principle) to make a very thin phtotodetector that has the same sensitivity with respect to light coming from either side, so that we can see interference between two light waves arriving from opposite sides? That is, as we vary the relative phase shift between the right hand...
  7. M

    Longitudinal/transverse modes in optical cavity (resonator)

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  8. G

    Dielectrics and standing waves

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  9. R

    I Normal modes in a coupled system

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  10. Twigg

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  11. S

    I Normal modes using representation theory

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  12. Mohamed_Wael

    How to eliminate modes in Ansys modal analysis

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  13. ShayanJ

    A UV and IR modes in ground state

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  14. S

    I Are quantum harmonic oscillators and radiation modes equal?

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  15. S

    Number of modes in optical fiber

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  16. K

    Mode matching (measured modes and modes obtained from FEA)

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  17. 1

    Help finding the vibrational frequencies and normal modes

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  18. A

    Why are there modes in cantilever beam oscillation equations

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  19. T

    Sound of vibrating string - modes

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  20. C

    I Are EH and HE Modes Simply Synonyms of LSE and LSM Modes?

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  21. Conservation

    I Calculating Modes in a Cavity: Why Use a Spherical Volume?

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  22. K

    Number of modes in Cubic Cavity

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  23. Tspirit

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  24. SuperSusanoo

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  25. Crush1986

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  26. AntonPannekoek

    I What is “normal” about normal frequencies and normal modes?

    So, my question is what does the "normal" part mean when one talks about normal frequencies and normal modes in coupled oscillations. Does it have to do with the normal coordinates that one uses when solving some problems, or with normal in the sense of orthogonal. Thanks for your help.
  27. C

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  28. F

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  29. M

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  30. RicardoMP

    Normal Modes and Normal Frequencies

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  31. S

    I Normal Modes: Finding Eigenfrequencies

    If I have a system where the following is found to describe the motion of three particles: The normal modes of the system are given by the following eigenvectors: $$(1,0,-1), (1,1,1), (1,-2,1)$$ How can I find the corresponding eigenfrequencies? It should be simple... What am I missing?
  32. B

    Relation between dimensional regularization and high-energy modes

    I state that I am a beginner in QFT, but it seems to me that the methods to regularize the integrals of the perturbation series before renormalize serve to cut off the high-energy modes that are responsable for the UV divergences. This ( the cut off of high-energy modes ) nevertheless is not so...
  33. E

    Modes orthogonality in a dielectric slab

    A typical mode in a dielectric slab like this, with propagation along x, uniformity along z and refractive index variation along y, is represented by the following function: f (y) = \begin{cases} \displaystyle \frac{\cos (k_1 y)}{\cos (k_1 d)} && |y| \leq d \\ e^{-j k_2 (y - d)} && |y| \geq d...
  34. S

    For a string with fixed ends, which normal modes are missing?

    Homework Statement Here's the problem. I was able to find the a_n and b_n values, my question is mainly on part (c), how do I find which modes are missing? The function is odd, so even modes should disappear, but cos(n*pi) doesn't disappear, it's either +1 or -1. I'd greatly appreciate any...
  35. N

    Normal modes and degrees of freedom in coupled oscillators

    Not a textbook/homework problem so I'm not using the format (hopefully that's ok). Can someone offer an explanation of normal modes and how to calculate the degrees of freedom in a system of coupled oscillators? From what I've seen the degrees of freedom seems to be equal to the number of...
  36. ChickenTarm

    How do I find the normal modes of massless string w/ masses?

    Homework Statement So, a string with length L and a mass of M is given tension T. Find the frequencies of the smallest three modes of transverse motion. Then compare with a massless string with the same tension and length, but there are 3 masses of M/3 equally spaced. So this is problem #1...
  37. F

    Are the vibration modes at the lattice centre odd or even?

    Homework Statement Good morning. I am currently doing an solid state problem; in this part, I have to tell if these vibration modes are odd or even. I am working at the lattice centre. The modes are these http://postimg.org/image/8nmv7ickz/. Homework Equations None The Attempt at a Solution...
  38. F

    Studying vibration modes of ice X

    Good afternoon. I am doing an study on ice X, a material with this structure http://postimg.org/image/nub4if9kb/ I want to know why in the centre of the brioullin zone the hidrogen atoms must remain at rest on an even mode. My reference book is Charles Kittle's, but there is no discussion about...
  39. G

    Laser TEM Modes - What Determines Output?

    What determines which TEM mode will the laser output have? Why some lasers emit in TEM00, while other in a donut mode, and other in a superposition of multiple modes. Thank you.
  40. S

    Understanding Coherent Large Scale Modes in Power Spectra

    Hi everyone, I am reading a paper, which discusses about power spectrum. There is a plot which is power versus k(wave number). It says something about "coherent large scale modes". Would you please tell me what the meaning of this is?
  41. fluidistic

    TM modes between 2 parallel plates with 2 dielectrics

    Homework Statement The space between 2 perfect conductor plates parallel to the x-z plane separated by a distance 2a are filled with 2 dielectric materials whose surface also lies in the x-z plane, at a distance equal to a from the plates. We're looking for TM modes propagating along the z...
  42. W

    Number of phonon modes possible

    Hi! How exactly is the relationship between number of atoms in the basis of a bravais lattice, and the number of possible phonon modes? So, for example, if you have 2 atoms in a basis you get 3 acoustical and 3 optical modes in 3 Dimensions. But why exactly is this? Do you need to set up the...
  43. F

    Question about gravitational waves, E modes

    Hi everybody, I have been reading about gravitational waves, but I don't get how the E modes work; in one place I read that they were created during the inflation time, but in other I read that they come from the recombination. Does it mean that they were produced almost when the Big Bang...
  44. O

    How to calculate the vibration modes of the beam?

    Hi, I´ve tried to calculate the vibration modes of beam in the space, without gravity or any other force. The forumle of the beam is this one: Cos(λL)*Cosh(λL)=1 from which I´ve calculate the roots and the resonance. I´ve found a programme for Matlab that calculates the vibrations modes if...
  45. J

    Understanding Modes in Fibre: Equations for Allowed Angles of Propagation

    So I've got the equation for 'allowed angles of propagation': SinΘp = pλ / 2πdnf With p is the mode, λ the wavelength, d the width and n the refractive index. I'm just not sure what to do with this equation, and my lecture notes don't go into any more detail. For example, if I knew the the max...
  46. J

    Why do small waveguides support less modes than larger ones?

    I've taken several courses on Electromagnetics and Waveguide. It has become common sense to me that small waveguides support less modes than larger ones. I've also learned the graphical method to calculate the number of modes in a 3-layer slab waveguide. What I don't get is why small...
  47. P

    Relating Behaviour of a Driven System to the Undriven Modes

    Is it generally true that if you have a system of particles with some arbitrary interactions due to their relative positions which you can solve in some way (maybe numerically, maybe analytically), you can relate the long term behaviour to the undriven case if it is being driven by a...
  48. S

    Finding the normal modes for a oscillating system

    Homework Statement The system is conformed by two blocks with masses m (on the left) and M (on the right), and two springs on the left/right has the spring constant of k. The middle spring has a spring constant of 4k. Friction and air resistance can be ignored. All springs are massless. Find...
  49. U

    Psi Meson Decay Modes: Spin, Parity, Quark Content & More

    Homework Statement (a) Explain spin and parity of mesons (b) State their quark content (c) Draw a feynman diagram of J/psi decay (d) Why doesn't ##\chi## undergo leptonic decay? (e) What is the minimum centre of mass? [/B] Homework EquationsThe Attempt at a Solution Part(a)[/B] Spin is...
  50. U

    Tau leptonic decay - Lifetimes and modes

    Homework Statement [/B] (a) Explain lepton universality. (b) Explain why decay mode is forbidden and find hadronic branching ratios. (c) Find the lifetime of tau lepton. (d) What tau decay mode would be suitable? (e) Find the precision. (f) How do you improve the results? (g) Why is it much...
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