Questions tagged [coupled-oscillators]
Harmonic oscillators may have several degrees of freedom linked to each other so the behavior of each influences that of the others. For example, two pendulum clocks (of identical frequency) mounted on a common wall will tend to synchronize. The apparent motions of the compound oscillations typically appears very complicated, but a more economic, computationally simpler and conceptually deeper description follows resolving the motion into [normal-modes].
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Decoupling Linearly Coupled Wave Equations with Potentials
I'm currently working numerically with wave equations and I was wondering if one can always decouple two wave equations, with potentials, which are linearly coupled. The system I'm talking about is ...
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Differences and similarities between phase transitions of Kuramoto model and thermodynamics
I am a math post-graduate (hardly have any modern physics background) and I'm considering the phase transition analysis on complex networks. To my knowledge, the Kuramoto model (see the wiki of ...
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Is there a generalization of mode coupling theory?
I am currently reading a lecture on coupled-modes theory and have a question regarding the ansatz:
$$E_\text{tot}=A(z)E_1(x,y,z) + B(z)E_2(x,y,z) \\ H_\text{tot}=A(z)H_1(x,y,z) + B(z)H_2(x,y,z)$$
and
$...
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How to demonstrate in a simple way that this system of differential equations form a damped harmonic oscillator? [closed]
How may I demonstrate in the most simple way that the following system of differential equation form a damped harmonic oscillator ?
$$
\dot x = -\alpha_x x - \omega y \\
\dot y = -\alpha_y y + \omega ...
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Does it make sense to talk about individual energies of interacting quantum particles?
Does it make any sense to talk about energy of any one particle in an interacting system? For example if we talk about a system of two coupled quantum harmonic oscillators of same mass and frequency, ...
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How to solve the coupled equation of motion? [closed]
there we have the EOM:
\begin{align*}
\alpha q_{2} + \lambda - \ddot{q}_1=0 \\
\alpha q_{1} + \lambda - \ddot{q}_2=0
\end{align*}
and $q_{i}$ is the canonical coordinates. Can I use the Fourier ...
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Coupled oscillators and stability of equilibrium points
My question is about parts (e) and (f). I have found the matrix to equation of motion to be $\frac{d}{dt}\begin{bmatrix} x_1 \\ x_2 \\ p_1 \\ p_2\end{bmatrix} = \begin{bmatrix} 0 & 0 & 1 & ...
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Do particles oscillating in coupled oscillation have only normal modes frequency?
If two bodies are coupled and they are performing oscillations, then do they have only two allowed frequencies (normal modes frequencies) with which they can oscillate or do they have a number of ...
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Why is this called a `Harmonic Oscillator Chain'?
Consider the following general setup:
Assume have a chain of atoms (of mass $m=1$) in one dimension interacting with their nearest neighbor through a interaction potential $U$, and which are in an ...
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Normal modes of three masses attached by two springs
I have the following system:
I've applied Newton's 2nd Law to the system and I have found the normal modes proceeding as an eigenvalues and eigenvectors problem. I obtained the frequencies $\omega_1^...
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Equations of motion for coupled harmonic oscillators
We just started QFT, and I'm following our professor's notes but there is a passage I do not understand. We are speaking about a system of $N$ coupled harmonic oscillators $y_j(t)$ for $j = 1, ..., N$ ...
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Coupled quantum harmonic oscillator: Decomposition in terms of number basis representation for numerical implementation
Consider the Hamiltonian of a coupled quantum harmonic oscillator
\begin{align}
\hat{H}&=\frac{1}{2m}(p_1^2+p_2^2)+\frac{m\omega^2}{2}(q_1^2+q_2^2)+\alpha(q_2-q_1)^2
\\&=\frac{1}{2m}(p_1^2+...
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Energy transfer between modes of linear chain of harmonic oscillators?
Consider a one dimensional chain of N classical point masses interacting with harmonic neighbor forces (with periodic boundaries for specificity). If the positions and velocities are prepared in a ...
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Does a chain of classical harmonic oscillators exhibit non-harmonic oscillations?
Consider a one dimensional chain of N classical point masses interacting with neighbor harmonic forces. Is it possible to find initial conditions (positions and velocities) such that non-periodic (...
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Normal modes of a circular array of interacting particles
I want to study the normal modes of an array of $N$ identical atoms placed in a circular lattice. The particles interact among them via Yukawa interaction potential,
$$\phi_Y(r)=\frac{A}{r}exp(-r/r_0)....
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