# 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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### Orthonormalization of eigenamplitudes

Assuming $(-\omega^2 \hat m + \hat k)\vec{a}=0$ where $\vec a$ is the eigenamplitude of the eigenfrequency $\omega$ , $\hat m$ is the mass matrix and $\hat k$ is the matrix of the potential constants. ...
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### Solving a system of three masses and two springs

Let's say $m_1$ is attached to $m_3$ via a spring of constant $k_1$ and $m_3$ is attached to $m_2$ via a spring of constant $k_2$. Just to simplify the problem we can make $m_1=m_2=m_3$ and $k_1=k_2$. ...
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### Double Pendulum - equation of angle with respect to time [closed]

First of all I am in grade 12, last year of my IB diploma programme. I'm familiar with derivatives and integrals but nothing as complex as these Lagrangians, Hamiltonians or other university-level ...
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### What is the generalised harmonic oscillator kernel?

So the kernel for the Lagrangian of the 1D harmonic oscillator: $$\mathcal{L} = \tfrac12 m \dot{x}^2 - \tfrac12 m \omega^2 x^2$$ is solvable (from the Wikipedia entry on Path Integral Formulation) ...
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### Why is energy usually concentrated on low frequency modes in dynamics?

In all structural dynamics applications I have seen, the motion is mostly governed by low frequency modes. For example, a pretty accurate approximation of buildings dynamics can be obtained with the ...
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