What is Normal mode: Definition and 24 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.
It's mentioned that the normal mode of molecule needs to involve the change in molecular polarizability to be Raman active.
Explanation is provided in Physical Chemistry textbook by Atkins on the example of the rotational Raman spectra. Only the frequency of the electric field ##(f_i)## occurs...
If a Hookean spring-mass system is made from one mass and a spring, to produce a system with a particular oscillation frequency, it's not a problem to use the propagation of errors concept to find how this frequency responds to small errors in the mass and spring constant. If a chain of...
What you think about this question?
Seems a little strange to me, that is, it considers the maximum kinetic energy when the displacement of the oscillators is maximum, i don't think this is right.
First I worked out the dispersion relations, which is pretty easy:
##M \ddot x_j = K x_{j-1} + K x_{j+1} - 2K x_j -mg \frac {x_j} {l} ## (All t-derivatives)
We know ##x_j## will be in the form ##Ae^{ijka}e^{-i\omega t}##
so the above becomes:
## -\omega^2M = K (e^{-ika}+e^{ika}-2)-\frac {g}...
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.
I think I miss something about energy of a mechanical wave.
In absence of dissipation the mechanical energy transported by an harmonic wave is constant.
$$E=\frac{1}{2} A^2 \omega^2 m$$
But, while studying normal modes on a rope, I find that the mechanical energy of a normal mode (still...
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...
On a test our teacher asked about a system composed of (string -> mass -> string -> mass) hanging, that began to oscillate up and down.
We all considered weight (mg) when applying Newton's second law to find the associated differential equation.
When we met our teacher again he said that we...
Homework Statement
Hey guys.
The title says it all pretty much. We need to find the normal mode frequencies of a driven/forced system containing 3 equal masses connected by 4 springs of equal spring constant k.
Homework Equations
F=m\ddot{x}
Spring potential
V = 0.5kx^{2}...
Homework Statement
Hi everyone! first post here :)
Basically, the question is as follows:
Consider a hydrogen fluoride molecule (atomic mass of H is 1g/mole and of F is 19 g/mole).
1. Write the energy of the system in terms of the displacements of both atoms.
There are other questions...
Hello,
My question stems from a research project of mine involving taking the normal modes of clusters of molecules from a potential. I was curious of the interpretation that can be made of normal mode vectors at a non-equilibrium structure, i.e something following a MD trajectory beginning at...
Hello,
My question stems from a research project of mine involving taking the normal modes of clusters of molecules from a potential. I was curious of the interpretation that can be made of normal mode vectors at a non-equilibrium structure, i.e something following a MD trajectory beginning at...
Homework Statement
The following circuit is given. C1=C2 L1=L2 R1=R2
I shall calculate the "normal mode" (I'm not sure if this is the 1:1 translation though) of the oscillation
Homework Equations
formula for electrical impedance and differential equations
The Attempt at a...
It is well known that for an isolated system, the normal mode frequency of a N-body harmonic oscillator satisfies Det(T-\omega^{2}V)=0. How about a non-isolated, fixed temperature system?
In solid state physics I have learned that in crystal the frequency does not change, but the amplitude of...
2 metal, thin, bars (length=l, mass=m) are hunging on same height (distance between bars-d)
Lower end of bars are conected by metal spring (mass=0, k-spring constant, d-length)
My problem is how to calculate a normal mode.
Homework Statement
A string that is fixed at both ends is vibrating in the third harmonic. the wave has a speed of 186m/s and a frequency of 225Hz. the amplitude of the string at an antinode is 0.0037m.
How much time does it take the string to go from its largest upward displacement to...
hi,im a newbie over here,my physics quite poor so i really need help by understanding it,i jz wanted to ask could any1 please explain to me what is in phase,&out of phase?;im totally baffled.:blushingAnd what's frequencies of the normal mode in standing waves in a string fixed in both ends?i...
What is the difference between eigenfriquency and normal mode? If, for example, I solve the secular equation (from the equations of motion) for a mechanical system (say two masses on springs) to obtain the eigenvalues I thought I got the normal modes, but now I am told I get the...
Homework Statement
A String of length L has one of its extremities fixed and the other one loose.
A. What's the equation for the normal mode frequencies?
B. Draw a snapshot of the string for the 1st 3 normal modes
Homework Equations
wave equation
The Attempt at a Solution...
Dear friends,
I need some help regarding running Gaussian 03. I have a complex molecule (64 atoms with 6 types of atom)...and finished geometry optimization successfully using method b3lyp with basis set pVDZ.. it took 4 days to complete this optimization procedure...Now i want to do frequency...
Hi Member,
does anyone have some experience with normal mode analysis?I need to know from basics...i want to use this analysis for finding the vibrations of a complex molecule...(may be by using Urey- force constants,etc..or if u know any other method !).
eagerly waiting
Rajini
Homework Statement
Two equal masses are connected by two massless springs of constant k and nat. length l. The masses are constrained by a frictionless tube on a pivot, (also massless) so that they remain colinear with the pivot. The pivot subtends angle theta with the vertical. The 1st mass...