# 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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### 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+...
1 vote
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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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### Does Hooke's law explain classical wave behavior?

Will Hooke's law $F = -kx$ applied to a large mass-spring grid array such as: provide the full and complete mechanistic explanation for classical wave behavior, including the 2nd order wave ...
1 vote
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### How to calculate the energy of a spring-mass system considering harmonic oscillation of the normal mode? [closed]

For a spring-mass system, we know that the potential and kinetic energy are $$E_p = \frac{1}{2}ku^2 \text{ and } E_k = \frac{1}{2}m\dot{u}^2.$$ where $k$, $m$ and $u$ are the spring constant, mass and ...
249 views

### Transfer function of system of coupled 2nd order ODE

I am wondering how to calculate transfer function $H(s)$ of system described by 3 coupled differential equations. The pourpose of work is to calculate "Bodedx" diagram ($|H(i\omega)|(\omega)$...
1 vote
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### Motion of an $n$ mass $n$ spring system [closed]

While reading wave motion I encountered the problem of $n$ identical masses with $n$ identical springs in between them. If we give a sudden push to the wall attached to the first spring, what will ...
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### Why is any arbitrary motion of a coupled oscillator writable as a linear combination of its normal modes? [duplicate]

Consider the following example of a coupled oscillator. Let two identical pendulums, each of length $\ell$ and mass $m$ be connected by a spring of force constant $k$. The system has two normal modes ...
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### How to describe a series of damped harmonic oscilators?

I am looking for textbooks or papers that provide an analysis for a series of damped springs. I am having a tricky time working out the details on my own. I know that if $F=-k\Delta x$ a series of ...
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### Equations of motion only have a solution for very specific initial conditions

An exercise made me consider the following Lagrangian $$L = \dot{x}_1^2+\dot{x}_2^2+2 \dot{x}_1 \dot{x}_2 + x_1^2+x_2^2.\tag{1}$$ If I didn't make a mistake the equations of motion should be given by: ...
1 vote
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### Coupled Oscillator Period [closed]

I was studying an example of a coupled oscillator the other day, namely two identical masses attached to three springs, the lateral ones of which with the same elastic constant, when I came across the ...
1 vote
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### Estimation of number of states to be used to obtain Wigner-Dyson distribution in a chaotic coupled oscilllator

A coupled harmonic oscillator with quadratic coupling - $$H = \frac{1}{2}(p_x^2 + p_y^2) + \frac{1}{2}(x^2 + y^2) + g x^2y^2,$$ is known to be non-integrable, hence chaotic (for reference look at ...
1 vote