Oscillators Definition and 161 Threads

Can someone help me with my code? I am trying to generate a lattice of harmonic oscillators, and I have written the following algorithm: for n = 2:((N-1)/h) a(1,n) = -(x0-(x(2,n)-x(1,n))); x(1,n+1) = 2*x(1,n) -x(1,n-1) + (h^2)*a(1,n); t(1,n+1) = t(1,n) + (h); for i =...

Homework Statement A system of 10 oscillators, characterised by a \beta^ parameter of ln(3/2) is in equilibrium with a heat bath. Determine the probability that the system should possesses Q quanta.Homework Equations p(Q) proportional to e^(-Beta*Q)The Attempt at a Solution I have seen a...

Homework Statement We consider a system of localized(in a lattice) weakly interacting harmonic oscillators having the non-degenerate energy levels: \epsilonv=(v+1/2)\hbar\omega v=0,1,2,... where the angular frequency is a function of the volume, \omega(V)=aN/V, where a is a constant...

Homework Statement Hi, I am revising for an exam, so this isn't really a homework question, but not sure which sub-forum it really fits on so its here. Anyway, I am trying to understand how a simple wein brige oscillator circuit works, as shown in the diagram...

Hello there! Could someone please help me with setting the starting equations for coupled oscillators. I'm having serious troubles with setting the +- signes right (yes, more than with the differental equations :) ). OFF TOPIC: any reading materials about problems with signs in physics will...

Ok, there's a bit I don't understand in my lecture notes. The maths doesn't seem to quite work out. Any help would be appreciated. Here's the section I'm confused about: http://img228.imageshack.us/i/physy.jpg/ It's the transition from the second last line of working to the last line which I...

Homework Statement I have solved for the eigenfrequencies of a system composed of two particles of masses m connected to each other by a spring of constant 2k and where one particle is connected to a wall by a spring of constant 4k and the other particle is connected to a second wall by a...

Homework Statement The problem: You are given the problem of analyzing the dynamics of a line of cars moving on a one-lane highway. One approach to this problem is to assume that the line of cars behaves like a group of coupled oscillators. How would you set this problem up in a tractable...

I'm doing a research project on collisions and I've come across a part of my theory that requires solutions to coupled damped oscillators. Could anyone please refer me to some text on 2 coupled damped oscillators which isn't extremely math heavy and has conceptual explanations of the...

i am having some problem in unerstanding a concept explained in my book in the chapter harmonic oscillators. as an example of this, it says, is the electromagnetic field, where A (vector potential) plays the role of the co ordinate and its dot plays the role of velocity in the oscillator...

Homework Statement Calculate the grand partition function for a system of N noninteracting quantum mechanical oscillators, all of which have the same natural frequency \omega_0. Do this for the following cases: (i) Boltzmann statistics; (ii) Bose statistics. Homework Equations The...

Hello, Basically, we were asked to verify the dependence of the period of an object attached on both ends by a spring upon the mass of this object in Simple Harmonic Motion. Therefore, using different masses, we calculated the period each time and made a graph where the period is a function...

Kind of new to this stuff, so hopefully you guys will bear with me. So a simple Oscillator with a Capacitor and Inductor... I understand that the energy flow causes the inductor to generate and collapse a magnetic field. I also understand that Sine waves are generated by changing the...

Does anyone know of a real system for which a collection of (weakly coupled) identical oscillators is a better model than it is for a solid? Diatomic gas molcules are a possibility, but I'm really looking for a system of distinguishable oscillators, which no doubt dictates oscillators at...

I think I did understand this once but now I am confused. If we choose the center-of-mass frame for a diatomic molecule, it also obeys the force law F=-kr, where r=(x,y,z), so why isn't it a 3-d harmonic oscillator, like an atom in solid? I know it may have something to do with the fact that gas...

For this question I'm not going to introduce the particular problem I am working on, rather, I am merely wanting some explanation of a concept which I can't seem to find in any of my textbooks. I suspect the authors think it is just too obvious to bother explaining :smile:. I'm revising for a...

Homework Statement Assume, you have an ensemble of linear harmonic oscilators, all having the same frequency \omega and amplitude a: x = a\cos(\omega t + \phi). The phase \phi is uniformly distributed in the inteval [0,2\pi). What ist the probability w(x)dx to find the displacement of one...

Homework Statement A system consists of 3N (N >> 1) independent, identical, but distinguishable one-dimensional oscillators. This is relevant in that the atoms in a solid are sitting around their equilibrium positions. Assume that every atom constitutes an independent oscillator and all...

Homework Statement An oscillator is driven by a triangular periodic force (if that makes sense), which has period \tau = 2. (a) Find the long-term motion x(t), assuming the following parameters: natural period \tau[naught] = 2 (that is, \omega[naught] = π), damping parameter ß = 0.1, and...

Homework Statement I am working on my lab, in which I have to find eigenvalues of coupled harmonic oscillators running a) in the same direction and b) in opposite directions. Two masses, three springs. --v^V^V^V^v--[M]--v^V^V^V^v--[M]--v^V^V^V^v- I have to compare my calculated values to...

Homework Statement 1. A 0.5 kg mass extends a spring 1 cm. What is the frequency of oscillation of this mass and spring? 2. A 1 m stick is used as a simple pendulum with a 3 kg weight on the end. What is its period of oscillation? 3. The same meter stick is used as a rigid pendulum with no...

In my textbook, it says "For a system of one-dimensional oscillators, the energy levels are equally spaced and non-degenerate, so the number of quantum states in an interval dE is proportional to dE so long as dE is much larger than the spacing h(h-bar)w between levels. In fact, we may conclude...

Hi I am new to this community, so don't beat me up too hard :). I have a question about the Hamiltonian when it will simulate the principal system as a harmonic oscillator interacting with the environment which is also an harmonic oscillator (page 291 in "Quantum computation and Quantum...

Homework Statement Please bear with me, I'm not that good with LaTeX. Consider the harmonic oscillator problem. Define \Phin(x) as the n-th wave function for one particle, with coordinate x and energy (n+1/2) \overline{h}\omega, where n=0, 1,… Now, let’s consider a system consisting of...

Homework Statement Given: The amplitude of a damped harmonic oscillator drops to 1/e of its initial value after n complete cycles. Show that the ratio of period of the oscillation to the period of the same oscillator with no damping is given by T(sub d)/T(sub o) = (1 +...

Homework Statement A system consists of N very weakly interacting particles at temperature T sufficiently high so that classical stat mech is applicable. Each particle has mass M and is free to perform one dimensional oscillations about its equilibrium position. Calculate the heat capacity...

Homework Statement The equation of motion for a particle of mass 1 in a quartic oscillator V(x)=0.25x^4 is x''+x^3=0. Suppose that the maximum amplitude of the oscillator is Xm(max). Find an expression for the time T that it takes to go from x=0 to x=Xm(max) and show that this time is...

A two-dimensional harmonic oscillator is associated with the group Su(2). What is that association? Solutions to the Dirac equation require a pair of spinors at each point? Can we think think of spacetime as having pairs of 2D harmonic oscillators at each point? Thanks for any help.

Homework Statement A carbon nanoparticle (very small particle) contains 5000 carbon atoms. According to the Einstein model of a solid, how many oscillators are in this block? I didn't know how to start, can anyone give me a suggesstion??

Microstates oscillators?? Homework Statement I have no idea where to begin on this problem. but here is what it asks Consider an object containing 6 one-dimensional oscillators (this object could represent a model of 2 atoms in an Einstein solid). There are 4 quanta of vibrational energy...

The problem is: A mass m and a mass 2m are attached to a light string of unstretched length 3l _{0} , so as to divide it into 3 equal segments. The string is streched between rigid supports a distance 3l \textgreater 3l _{0} apart and the masses are free to oscillate longitudinally. The...

Ok i know that the solution for the harmonic oscillator differential equation is x=Acos(wt+d) However, I also know that most of the time, atleast in average intermediate mechanics problems the phase difference, d is zero. this baffles me a lot. for example if there is a spring and i...

Two different simple harmonic oscillators have the same natural frequency (f=3.40 Hz) when they are on the surface of the Earth. The first oscillator is a pendulum, the second is a vertical spring and mass. If both systems are moved to the surface of the moon (g=1.67 m/s^2, what is the new...

Hi folks, I have to solve an exercise about two oscillators whose Hamiltonian is H = 1/2 (m w^2 q1^2 + m mu^2 w^2 q2^2 + m lambda^2 w^2 q1 q2) I successfully found the unitary transformation that decouples the problem, but I am also asked to use the Adiabatic Method to find approximate...

Hi there I need some advice, please: can you suggest any interesting cases of a driven, damped harmonic oscillator? I need to write a report (part of some assignment) on the mathematical model/behaviour/etc. of some real-world driven oscillator. No problems with the math, I'm just looking...

[SOLVED] potential of coupled oscillators Homework Statement http://cache.eb.com/eb/image?id=2480&rendTypeId=4 How do you calculate the potential energy of the coupled oscillators in the picture with spring constant k_1,k_2,k_3 as the spring constants from left to write?Homework Equations The...

Homework Statement The number of microstates of a system of N oscillators containing Q quanta of energy homework is given by W(N,Q) = (N+Q-1)!/[(N-1)!Q!] Show that when one further quantum is added to the system the number of microstates increases by a factor of approximately (1+N/Q)...

Homework Statement For a certain oscillator the net force on the body with mass m is given by fx = -cx^3. One-quarter of a period is the time for the body to move from x=0 to x=A. Calculate this time and hence the period. Express your answer in terms of the variables A, m, and c...

Hello all. I am having a substantially difficult time with what should be, actually, a very simple problem. I have three masses, each with a spring on each side (so three masses and four springs total in the system). My problem is writing down the equations of motion. I can do it when...

Homework Statement A particle of mass m1 is attached to a wall by a spring of constant k. A second particle of mass m2 is attached to a different wall by another sping of constant k. The two masses are attached to each other by a third spring of constant k. Let x_1 and x_2 be the displacement...

Homework Statement If the probability of finding a system in any microstate is the same, how can we say there is a most probable distribution energy among the oscillators in the system?Homework Equations None for this particular question.The Attempt at a Solution Since the interatomic potential...

Consider an object containing 9 one-dimensional oscillators (this object could represent a model of 3 atoms in an Einstein solid). There are 5 quanta of vibrational energy in the object. (a) How many microstates are there, all with the same energy? 1287 microstates (b) If you examined a...

A carbon nanoparticle (very small particle) contains 8000 carbon atoms. According to the Einstein model of a solid, how many oscillators are in this block? I have no idea where to even begin, can someone point me in the right direction?

Hi there I've heard from various applied mathematicians that the D.E. that models harmonic motion is one of the most important in physics...apparently it appears in nearly every conceivable field, from quantum mechanics to cosmology (something to do with modelling the cosmic microwave...

Hey, I'm just having some trouble getting started with this problem. ------------- ( ) ( m1 ( ) ( 2m1 Crude representation: (The parantheses are supposed to be the springs) There is a mass (m1) that is attached vertically to a board by a spring of...

I have been learning oscillations this sem and found solving system of coupled oscillators a very common subject in this course.. I want to know if the procedure is always:(can be either a spring sys or pendelum system..) 1.lay down n equations for n coupled oscillators including Xn and w and...

First of all, why is E = h\nu? Second, where can I find the derivation behind Planck's "oscillators in a box" calculations that led to the assumption that energy is quantized? I realize that my questions are a bit vague, but I cannot make them more specific as I do not have a firm grasp of...

Homework Statement Consider two coupled oscillators. The Hamiltonian is given as H=p1^2/2m + p2^2/2m +1/2m*omega^2*[x1^2+x2^2+2*lambda*(x1-x2)^2] Separate the center of mass and relative motion and find the eigenfunctions and eigenvalues. Homework Equations relative coordinate ...

Homework Statement The question then goes on to say: Decompose the resulting oscillation as a superposition of symmetric and antisymmetric mode oscillations. Hence give A and B in terms of C Homework Equations The Attempt at a Solution Well as of yet I'm not sure I fully...