# 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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### Coupled-mode theory and slowly varying envelope approximation

I am facing a situation where I have the following coupled-system equation: $\dot{U}(z) = i \; M(z) \cdot U(z) \quad ,$ where U is a N-vector and M is a NxN matrix. Now, the diagonal elements of M ...
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### If two pendulums connected by a spring both following Simply Harmonic Motion - why do they need the same time dependence?

I was reading a section of Introduction to Mechanics by Kleppner and Kolenkow: where it talks about the same time dependence. I'm not very familiar with this term but was wondering if there was some ...
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### Equations of motion of two bodies attached to three springs

I've been tasked with describing the equations of motion of two bodies attached via three springs, as visualized below. Let $x_1(t)$ and $x_2(t)$ denote the $x$-displacements of boxes $m_1$ and $m_2$ ...
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I have come across a coupled nonlinear dynamical system given below $$r\, \ddot{x} + \dot{x} = \sin y~,$$ $$r\, \ddot{y} + \dot{y} = \sin x~,$$ where $r$ is some real number and $\dot{x}$ denotes $\... • 21 1 vote 0 answers 196 views ### What are normal modes? In normal modes analysis the differential equations of the system are Fourier transformed and the Fourier monochromatics are found. I think these monochromatics are usually called normal modes of the ... • 1,904 -1 votes 1 answer 84 views ### Use Hamilton's principle to show expression for$L\$ [closed]
I have following diagram I have here to find the kinetic energy and the potential energy. I think that kinetic energy is: $$T=\frac{1}{2} M(\dot{x_1}^2+\dot{x_2}^2)$$ and the potenitial energy must ...