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.
Let's take for example the decay K+ -> pi+,pi0,gamma
This can proceed via direct emission or inner bremsstrahlung. I have questions for each of these modes
1. For inner bremsstrahlung, it is a final charged product that radiates, correct? In this case the pi+. What is causing the...
Hi
Can someone help me with the following questions please (see attachment)?
I really need some help on the following:
i). Drawing a force diagram for each particle (I really hate drawing these).
As a guess for m1, am I right in thinking that H and N point up and W points down? But...
Assume that a narrow layer of the sun just below the photosphere is modeled by an isothermal layer of neutral hydrogen and helium at 8000K below which is a fully convective layer with adiabatic sound velocity increasing linearly as a function of depth with a scale length of 100 km
a.) use the...
[SOLVED] Springs, Normal Modes, and Center of Mass coordinates
1.) Problem
The problem of the linear triatomic molecule can be reduced to one of two degrees of freedom by introducing coordinates y_{1} = x_{2} - x_{1}, y_{2} = x_{3} - x_{2}, and eliminating x_{2} by requiring that the center...
If I have a finite boundary, say of length L. Is it possible to demonstrate that if I were to allow all possible CONTINUOUS values of a wave to exist (with unit amplitude) then deconstrutive interference destroys all waves except those with wavelength:
k=\frac{n\pi}{L}
Where n =0,1...
Hello
I'm looking for a list,as complete as possible, of decay modes and their probabilities, for all known subatomic particles.
I've been googling, but found only bits and pieces. Perhaps someone knows a place on internet, or has found a free document to share, or anything like that
thanks
Homework Statement
Hello,
This is more of a conceptual question rather than a problem with numbers.
I was wondering if anyone new if there is a relationship between axial, tortional and pendulum vibration. The context is a mass hanging off a spring.
ie will the natural frequency of...
Homework Statement
hey, this is my first time using this forum and was wondering if i could have some help with this normal modes question.
suspended from a ceiling is in order: a spring of spring constant (k_{2}), a mass (m), a spring with spring constant (k_{1}), and another mass (m)...
Homework Statement
What is the difference between a mode and a node
The Attempt at a Solution
I am not really sure, because they seem exactly the same to me. Any help would be much appreciated!
I am trying to determine some failure modes of strain gauges and the means of accomplishing some of them. Things like loose leads, debonding, physical damage, thermal effects, doing things that cause saturation.
I am looking for ideas of what other failure modes are and ways to accomplish...
I Have a question that is bugging me because I can't get the answer out here's the question:
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...
I Have a question that is bugging me because I can't get the answer out here's the question:
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...
I am attempting to model a multi-mode symmetrical slab waveguide using Fortran 90. I am able to produce plots of each optical mode and am then summing them but I am more or less convinced that the relative intensity of the modes is incorrect. I am fairly sure that the error is arising because I...
Homework Statement
Discuss the motion of a continuous string when the initial conditions are q'(x,0) = 0 and q(x,0) = Asin(3πx/L). Resolve the solution into normal modes. Show that if the string is driven at an arbitrary point, none of the normal modes with nodes at the driving point will be...
Hello all,
if I have incoming radiation from a blackbody source filtered to a bandwidth of 0.1 nm and centered at a wavelength of 500 nm, why is the number of modes in this light not equal to the density of photon states times the bandwidth?
I.e why isn't it
\text{number of modes} = g(\omega)...
Can anyone point me to an online resource which gives details - and applications - as to when one should model an optical field using TE and TM modes, and when it's OK to use TEM modes.
Cheers.
edit: should've stuck this in the normal physics forum... mods please move...
More specifics...
Hi
see the attached picture...
2 coupled masses, each suspended from spring in gravitational field...
also entire construction can vibrate only vertically...
I need to write lagrangian for this system in the following form...
I have just been solving some systems of ODEs to find the nomal mode solutions. Something about it has been bugging me though.
In a simple case where we have a system of two linear ODEs representing a two-mass spring system, we assume that the solution is a normal mode and so find a general...
I've read that the extra dims are stabilized via string winding modes -
This is a bit of a star trek style question but is it theoretically possible to somehow 'interfere' with the winding modes so as to CHAGNE in some way the size of an extra dimension.
I'm really interested in this - if...
Hello,
I'm preparing for my condensed matter exam and I'm trying to solve problem 3a) of chapter 22 in Ashcroft & Mermin. The problem is basically to prove that the dispersion relation of a diatomic linear chain will reduce to the monoatomic one when the coupling constants are equal...
Hi,
I have a few questions about Sonometers which I've attempted to think through - though I may be missing something. Perhaps someone can fill in any gaps for me?
If I was to be asked why only 'discrete modes' of vibration can exist for a sonometer, is it enough merely to talk about the...
This might be a bit to specalised for some of you, but i am trying to calculate the number of modes that light can propegate in a material. The question is as follows
Consider a cavity that is a cube with the side length a = 1mm filled with water (refractive index(n) 1.33). Calculate the...
from C.Z. Tan, Optical interference in overtones and combination bands in \alpha-quartz, Journal of Physics and Chemistry of Solids 64 (2003) 121–125.
[1] M. Born, K. Huang, Dynamical Theory of Crystal Lattices, Clarendon Press, Oxford, 1988.
[2] C. Kittel, Introduction to Solid State...
Trying to do some reading on squeezed electric field modes in accelerated frames, and it's a bit much. Anyone have any suggestions as to some literature to familiarize myself with before i go any further? Thanks
Phil
I have a book here that says that the number of normal modes is equal to the number of degree of freedom of a system. I'm wondering if this applies to just about any system or only to systems in which every coordinates can oscillate harmonically. The question is not very well formulated, so I...
Dear friends,
I'm having trouble with this problem, I don't know if I'm doing it right, I'd be grateful if you could advice me.
Two discs, each of mass M and radius R, are supported with equal
separation along a slender rod to which they are rigidly fastened at
their centers as shown in...
urgently need help: localized modes in linear chain and localization effects
Hello everyone, it is great place you have here, hope I can learn a lot from you
I am doing some readings and there are couple of concepts that I havent
been familiar with and if you spend a little time to help me...
Could someone please tell me how I could calculate the vibrational modes of a solid sphere, or where I could find this information? I want to make the calculations for a sphere with a unit radius.
When I was viewing some photos about rocket engines (spatial ones), I wondered me in what mode is operating the nozzle in the normal working.I am going to try to explain it better (do not show me a strange face yet). I studied the different exhaust modes of a convergent-divergent nozzle...