# What is Modes: Definition and 281 Discussions

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. ### Normal modes of four coupled oscillating masses (Kleppner and Kolenkow)

This exercise comes from Kleppner and Kolenkow, 2nd ed., problem 6-3. I'm using a solution key as a study reference, but the solution key is coming to a pretty different conclusion. Mostly the issue is in the equations of motion for this system. I'm not sure if there's something I'm...
2. ### MATLAB FEM, Matlab and the modes of an element

Hello I wrote a Matlab code to form the 8 by 8 stiffness matrix of a single, 4-noded element, for a plane strain problem for an isotropic element. I conduct an eigenvalue analysis on this matrix Matlabe reports 5 non-zero eigenvalue modes, and 3 zero-eigenvalue modes (as expected) Of the 3...
3. ### A How do we derive the number of string excitation modes for large N?

On page 52 in Becker, Becker, Schwarz, there is an equation (2.148) for the number of open string excitation modes. I tried to Tayler expand eq 2.145, but couldn't reproduce 2.148. Plus, one gets 2.145 by setting w close to 1; even if I use the 2.146 and try to analyze it around 0, I am still...
4. ### I Majorana zero modes observed by Microsoft?

https://arxiv.org/abs/2207.02472 InAs-Al Hybrid Devices Passing the Topological Gap Protocol "We present measurements and simulations of semiconductor-superconductor heterostructure devices that are consistent with the observation of topological superconductivity and Majorana zero modes."...
5. ### Normal modes of oscillation

The first part is trivial not sure where to go on the second part.
6. ### Normal modes: Spring and pendulum

I was doing the exercise as follows: I am not sure if you agree with me, but i disagree with the solution given. I was expecting that the kinect energy of the mass ##m## (##T_2##) should be $$T_2 = \frac{m((\dot q+lcos(\theta)\dot \theta)^2 + (lsin(\theta) \dot \theta)^2)}{2}$$ I could be...
7. ### I Find the interference function for different emission modes

Homework Statement:: Find the interference function ##I(\delta)## where The emission is analyze by a Michelson interferometer. Relevant Equations:: ##I(\delta) = \frac{1}{2} \int_{-\infty}^{\infty} G(k) r^{ik \delta} dk## ##I(\vec{r}) = I_1 + I_i + 2 \sqrt(I_1 I_i) cos (k\delta)## I have 5...
8. ### Finding Total Number of Optical Field Modes for Visible Light

ρ_kdk = k^2/π^2 dk is the density of field modes (what we are trying to solve for here), and as ρ_kdk = ρ_λdλ, and k=2π/λ, we can rearrange this to get ρ_λdλ = 8π/λ^4dλ This is where my confusion lies. I am not sure what to do next. I know this equation physically means the number of modes per...
9. ### A Propagation modes and linear systems

In the book "Fundamentals of photonics", the authors defined waveguide modes using the notion of linear systems, where they said: "Every linear system is characterized by special inputs that are invariant to the system, i.e., inputs that are not altered (except for a multiplicative constant)...
10. ### Vibrational Modes: How They Affect Motion

Ps: It is not a homework hence why I did not leave it under that headline.
11. ### A Angularly Propagating Modes In a Cylindrical Waveguide

Hey all, I was citing a result from a review paper in my paper, and I think it's wrong. I would really appreciate an outside perspective if anyone has the time! The result was for the electric field outside a metal rod (cylindrical waveguide, if you prefer) in vacuum. Here's the picture (you...
12. ### A Unruh & Minkowski Modes: Analytic Extension Explained

In Carroll "Spacetime and Geometry" I found the following explanation for why the analytically extended rindler modes share the same vacuum state as the Minkowski vacuum state: I can't quite understand why the fact that the extended modes [\tex]h_k^{(1),(2)}[\tex] are analytic and bounded on...
13. ### Medical Different types fluoroscopy modes in X-ray imaging?

what is fluoroscopy mode in cardiac xray imaging?. simulator shows EP,LF,MF,HI(extra low fluoroscpy, low, medium and highfluoro.what is it actually means?
14. ### Analysing the Normal Modes and Dynamics of a Cluster of Atoms

I am trying to analyse the dynamics of a cluster of 79 atoms. The system can be described with: ##\omega^2 \vec x = \tilde D\vec x## Where ##\omega^2## (the eigenvalues) are the squares of the vibration frequencies for each mode of motion, ##\tilde D## is the "dynamical matrix" which is a...
15. ### Modes in a cylindrical dielectric waveguide

I pretend to use the ecuation twice, once for the interior and another for the vaccum, so if I use the cilindrical coordinates for \nabla_t^2 it results in two Bessel equations, one for the interior and another fot the vaccum. In the vaccum, the fields should experiment a exponential decay, in...

36. ### A Equipartition of energy in the modes of a resonant cavity

I think the answer for this may be straightforward, but I don't see anywhere that explains this from the scratch: A large resonant cavity with a small hole is used to approximate an ideal black body. I understand the conditions for the modes inside the cavity. But there are two points that...
37. ### I How to find the most likely modes of decay for a particle

What are the most likely modes of decay for ##\Omega ^{-}## into 2 hadrons? ##BR_{k}=\frac{\Gamma _{k}}{\Gamma}## ##\Gamma=\frac{\hbar}{\tau }## ##\Gamma _{k}=\Gamma _{if}=2\pi \rho|<\Psi _{i}|H_{Int}|\Psi _{f}>|^{2} (E_{f})## I took a look at the Particle Data Group, and the most likely modes...
38. ### Modes and Q-factor(s) of a random laser

Many papers about random lasers mention the Q-factor of random lasers. Since a random laser has multiple peaks close to each other like shown in the figure. Does each of these peaks correspond to a unique random lasing mode, or is it just a single mode? Similarly what is the right way to...
39. ### Jackson E&M: Power loss in waveguides for TE & TM modes

Hi. I'm having trouble with calculating (8.59) from (8.58) (## \vec H_{//} ## is simply ## \vec H ## in Jackson, but that shouldn't matter.) in Jackson. Specifically I think I'm not sure about parallel component of H field here. For example, shouldn't I have two terms for the...
40. ### Decay modes and lifetimes of hydrogen metastable states

Protium atom has two low lying excited states with long lifetimes. These are: 2s. Decay energy would be 121 nm, but forbidden (no angular momentum difference). Fastest allowed decay is two-photon emission, lifetime 0,15 s Triplet 1s. Decay energy 211 mm. Prevalent decay single photon emission...
41. ### The number of vibrational modes g(v)dv in Debye theory

Homework Statement Show that, in the Debye theory, the number of excited vibrational modes in the frequency range ##\nu## to ##\nu+d\nu##, at temperature T, is proportional to x2e-x, where ##x=h\nu/kT##. The maximum in this function occurs at a frequency ##\nu'=2kT/h##; hence ##\nu'→0## as...
42. ### I Radioactive decays, different modes share

Hello, I'd like someone to help me understand, how can I tell from available data, what is the approximate share of different decay modes, for some given nuclide activity. Let's take 90Y for instance. It's known for being beta-emitter, but it emits gammas and X-rays as well. How to...
43. ### A Calculating decay rates for modes of a circular membrane

I am trying to solve for the theoretical relative decay rates of the various (m,n) modes of an ideal circular membrane, if that membrane is excited momentarily by an impulse or deformation. I would ideally like the decays of the (m,n) modes in dB/s. Imagine a simple isolated drum head being...
44. ### Modes of Optical Fiber propagation

What actually is a mode of optical fiber propagation?Is it similar to modes which correspond to various configurations as in standing waves on a string ? Also How correct is it to consider no. of rays as no of modes?
45. ### Normal modes of a system of springs

I'm looking at what should be just a simple spring system where four identical springs are holding up a square, load-bearing pallet plate in a warehouse. Now, someone says the equation of motion for the vertical normal mode of vibration is simply d2z/dt2 = -4(k/m)z. Right away however, I see no...
46. ### Confusion about two modes of coupled oscillators having same frequency

I am studying coupled oscillations and one of the refrance I'm using says that two modes can have same frequency whereas the other one says it's impossible to have same frequency for two modes. Please help.
47. ### A Are vacuum EM modes circularly polarized according to QED?

I'm talking of the virtual EM modes of vacuum...
48. M

### A What are the oscillation modes in low-gravity capillary-dominated flow?

Hi PF! I am solving a problem for low-gravity capillary-dominated flow, where liquid rests in a rectangular (2D) channel. The text I'm reading introduces a velocity potential ##\hat u = \nabla \phi##, and then states that each oscillation mode is ##\partial_n\phi|_\Gamma = \nabla \phi \cdot...
49. ### Define the polarization in TE/TM modes

Hello people, I'm a little bit confused about how to define the polarization direction for TM/TE mode. Take a look at the TE mode picture I found in some place. Picture1 The Cartesian system of coordinate (XYZ) here is chosen by the right hand rule. Picture2 But how we chose the direction...
50. ### A Calculating Vibration Modes of a Cylinder (Drum Shell)?

I am working on some acoustic synthesis models of real world instruments. The Bessel Function zeros give the vibration modes of a circular membrane, which can be used to model a drum head or even roughly a cymbal. However, much of a drum's sound (especially snare) comes from the "ring" of the...