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. fluidistic

    Normal modes for small oscillations

    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...
  2. D

    Why are there only limited modes of radioactivity?

    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...
  3. C

    Heat transfer: All 3 modes together

    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...
  4. Simfish

    Double Pendulum and Normal Modes (Kibble problem)

    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...
  5. L

    (Small oscillations) Finding Normal modes procedure.

    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...
  6. T

    Modes of Propagation in an Optical Fibre

    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...
  7. H

    Nambu Modes: Necessary & Adequate Condition of Symmetry Breaking

    Dear all, I have a question regarding the usual Goldstone theorem, which states that, for a system with continuous symmetry breaking, massless bosons must appear. However, if you look at the derivations of this theorem [1], the crucial assumption seems that, the conserved quantity associated...
  8. S

    Laser Modes & Spectral Hole Burning

    Homework Statement Reflection at a surface takes place under the condition that the field amplitude is zero at the reflecting surface. As a result, the axial modes i of wavelength λi inside a laser cavity can be defined by their number ni of sine-wave half cycles that fit exactly into the...
  9. D

    Vibration related: Rigid body modes

    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...
  10. W

    Coupled oscillators and normal modes question

    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...
  11. M

    How Do Transverse Modes Shape Laser Beam Profiles?

    Hi, I'm trying to get my head around the concept of transverse modes as seen from the outputs of lasers. I'm really struggling to even visualise the concept. From what I grasp, the transverse mode represents the intensity profile of the output laser beam. However I just can't make the jump...
  12. S

    Can gravity be ignored in a spring problem with multiple masses and springs?

    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...|...
  13. J

    Finding frequencies of normal modes with the systematic method

    I am having problems understanding the "systematic method" for determining the frequencies and amplitude ratios of normal modes when a system has more than one degree of freedom. I think I initially have problems setting up the differential equation that describes the motion. Here is the...
  14. V

    What is the range of angular frequencies for this waveform?

    I've attached the problem sheet with the given bottom line numerical answers. I'm struggling with question 3 part d and the solution sheet doesn't include the answer to this part of the question. I've completed the previous parts to question 3 already. Can someone please guide me through...
  15. B

    Normal modes of square membrane

    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)...
  16. T

    Understanding Normal Modes of Light Propagation in Anisotropic Crystals

    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...
  17. M

    Normal modes in a acoustic chamber

    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...
  18. S

    Fermat's Principle, Fourier Analysis, Standing waves, Normal Modes

    Can someone provide me a link that explains and provides a proof for the following principles: 1. Fermat's Principle that light always takes the path that minimizes the time taken 2. Solution to a Fourier Series and why all periodic motion can be represented as an infinite sum of sines and...
  19. M

    Sum of Normal Modes on a Vibrating String

    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...
  20. S

    Trying to calculate normal modes of nearly infinite network LC circuits

    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...
  21. Q

    Resonant modes of simply supported square plate

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

    Thermal Field Theory Integration over the modes?

    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...
  23. R

    Uncovering the Mystery of Soft Optical Modes

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

    Exploring Fe-H and Fe-D Modes: Seeking Answers

    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
  25. K

    Trimolecular system (normal modes)

    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.
  26. MTd2

    Are there collective modes on Spin Foams or LQG?

    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
  27. D

    Collective modes and restoration of gauge invariance in superconductivity

    After the first explanation of superconductivity by Bardeen, Cooper and Schrieffer, it was for several years a matter of concern to render the theory charge conserving and gauge invariant. I have been reading the article by Y. Nambu, Phys. Rev. Vol. 117, p. 648 (1960) who uses Ward identities to...
  28. T

    Orthogonality between optical fibre modes

    Hi there, I've just read the following: The expression that is given is: \int_{A \infty} e_j \times h_k* \cdot \widehat{z} dA = 0 where * denotes the complex conjugate, and z^ is the unit vector in the direction of propagation (along the axis of the fibre). Can anyone explain...
  29. N

    Carbon dioxide as an oscillator; normal modes.

    Homework Statement Consider the CO2 molecule as a system made of a central mass m_2 connected by equal springs of spring constant k to two masses m_1 and m_3 a) set up and solve the equations for the two normal modes in which the masses oscillate along the line joining their centers (the...
  30. X

    Can Eigenfrequencies Explain Oscillatory Behavior in this Dynamical System?

    1. Homework Statement Someone studying a dynamical system in another field of science tells you that when they attempt to model the experiment they’ve been examining they obtain the following set of coupled ordinary differential equations. \dot{x}= -Ax + By \dot{y}= -Cx In what follows you...
  31. D

    Under free vibration does it vibrate in all the modes

    say a system has 3 modes. under free vibration does it vibrate in all the modes all just one mode? why. also if we apply a either a impulse or pulsating force to the system, in which modes the system is going to vibrate and why? thanks.
  32. S

    Normal modes of a string NEED HELP

    A string with one end fixed as U(x=0,t)=0. The other end is attached to a massless ring which moves frictionlessly along a rod at x=L a) Explain the boundary condition at x=L should be d/dx U(x,t) = 0. b) Find the normal modes for the wave equation d2/dt2 U(x,t) = c2 * d2/dx2 U(x,t) with the...
  33. X

    Normal modes of Mass and two Spings

    Homework Statement Consider a mass M whose motion is confined to a flat, smooth two-dimensional surface. Label the locations in this surface using the Cartesian coordinates (x, y). The mass is attached to two identical springs, each of length ℓ and spring constant k. One spring has one of its...
  34. P

    Normal Modes - Pendulum on a Moving Block

    Homework Statement A block of mass M can move along a smooth horizontal track. Hanging from the block is a mass m on a light rod of length l that is free to move in a vertical plane that includes the line of motion of the block. Find the frequency and displacement patterns of the normal...
  35. P

    What Are the Normal Mode Frequencies of a Rod on a String?

    Homework Statement A uniform rod of length a hangs vertically on the end of an inelastic string of length a, the string being attached to the upper end of the rod. What are the frequencies of the normal modes of oscillation in a vertical plane? Answer: \omega^2 = (5 \pm \sqrt{19})g/a...
  36. Y

    Characteristic modes of oscillation of three masses on a hoop

    Homework Statement Three beads of equal mass m are constrained to lie on a circular hoop of radius a = 1. The beads are connected by identical springs of spring constant k. The equations of motion for displacements are (I am going to use x, y, and z, where x = theta 1, y = theta 2, z =...
  37. K

    TE/TM modes in idelectric waveguides and their effect on light output

    Hello everyone, I just have a few questions concerning TE and TM modes in a dielectric slab symmetrical waveguide. 1) How do the TE and TM mode profiles affect the actual light pattern being output on the waveguide face/facet? What determines the actual light patterns on the waveguide face...
  38. F

    The Meaning of TM11 and TE10/TE01 Modes

    Why is the lowest order TM and TE mode TM11 and TE10(or TE01)? What is the physical meaning of the different orders of the modes? Thanks.
  39. C

    Calculate number of modes incident on detect from black body

    Homework Statement In an experiment to measure photon statistics of thermal light, the radiation from a black-body source is filtered with an interference filter of bandwidth 0.1 nm centered at 500 nm, and allowed to fall on a photon-counting detector. Calculate the number of modes incident on...
  40. Spinnor

    Massive and massless modes of the anchored string.

    An anchored string is a simple modification of a vibrating string. We imagine a sideways restoring force applied to a vibrating string. The sideways force per unit length is proportional to the displacement of the string. This additional force gives the string the the same dispersion curve as...
  41. I

    How Does Cramer's Rule Apply to Finding Normal Modes in Oscillatory Systems?

    Homework Statement I'm reading Landau's Mechanics, in section 23, he discusses the oscillations with more than one degree of freedom, the Lagrangian is L = \frac{1}{2}\left(m_{ik}\dot{x}_i\dot{x}_k - k_{ik}x_ix_k\right) where m_{ik},k_{ik} are symmetric constants, and the summation over...
  42. M

    Quantizing Zero-Frequency Modes: A Challenge

    Let's say you want to quantize the EM field in a system with real permittivities and permeabilities. You expand the fields into a superpositions of their classical modes, and note that pretty much every real spatial mode requires two real conjugate canonical variables to describe its time...
  43. Q

    Waves, Energy, Blackbodies and Modes

    I am going over some notes and am trying to fit some pieces together. For some reason I keep confusing myself as to what exactly a "mode" is. Is a mode a wave? or a frequency? Also, how does a mode relate to the degrees of freedom for a particle in a system? Thanks!
  44. A

    Oscilloscope Modes: Understand Different Types

    I don't know if this the right forum to post this question but i can't figure out which forum i should use:confused: here is my question What are the modes in Oscilloscope? i did google search but couldn't find clear answer for my question. thanks
  45. W

    Three pendulums, two springs normal modes.

    I have a coupled oscillator system that is three pendulums attached together by two springs. The first part of the problems asks to argue, using symmetry arguments, that there are two "obvious" normal modes: one with w^2=g/l and another with w^2=g/l + k/m. I understand that these two frequencies...
  46. C

    Modes of vibration, natural frequency

    Hi.. I have a question about natural fvibration. Every object has natural frequency and modes of vibration. Let us consider a simple cantilever beam for our discussion. and Let's say its first 4 modes of vibration are at 3, 6, 10 and 20 kHz respectively. (I made up these frequency values)...
  47. N

    Waveguiding, Modes, Organic LEDs

    Hi everyone, I was wondering if someone could please explain to me the concept of waveguiding, coupling/coupled, and guiding mode. Here is an application of these terms: The photons emitted in the active region of OLEDs are coupled into three types of modes: direct transmission into...
  48. P

    Resonance ans normal modes in an open pipe

    Hello, I have a question about standing sound waves in an open pipe caused by a speaker, I know that normal mode frequencies are given by f_n = n\frac{v}{4L}, \quad n=1,2,3,... if we put a microphone into the pipe, and if the frequency of the speaker is a normal mode frequency, we see...
  49. B

    Normal Modes & Frequencies for Suspended Spring System: Masses 3m & 2m

    Homework Statement A particle P of mass 3m is suspended from a fixed point O by a massless linear spring with strength alpha. A second particle Q of mass 2m is in turn suspended from P by a second spring of the same strength. The system moves in the vertical straight lie through O . Find...
  50. D

    Theory of Vibration and Normal Modes

    I'm looking for an in depth and comprehensive treatment of the theory of normal modes; any suggestions?
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