# 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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### 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 ...
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### Conceptual Question of Small Oscillations of Coupled Harmonic Oscillators - Classical Mechanics

Is my following understanding of small vibrations correct? Modal matrix is the transformation matrix that relates general coordinates and the normal coordinates Normal coordinates are the linear ...
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### 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 ($|H(i\omega)|(\omega)$...
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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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### Terminology question: in-phase or out-of-phase?

Suppose that in a chain of many coupled oscillators, the displacements of two consecutive particles, in a normal mode of oscillation with frequency $\omega$, are given by $$x_p(t)=A_pe^{i\omega t}$$ ...
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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: ...
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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 ...
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### How to perform a Gaussian functional integral?

I'm completely beginner to the quantum field theory and try to learn the basics of functional integrals. However, I could not understand clearly. Could someone please explain the idea with the help of ...
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### Intuitive understanding of the resonance of a bridge

Dynamics of strides, walking and corresponding force cycles: In the civil engineering literature, it is known that the resonant frequency of a bridge should not be the same as that of the strides of ...
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### Difference between reactive (coherent) and dissipative coupling in open quantum systems?

I am unsure about the physical interpretation of the different types of coupling, I understand that reactive coupling is manifested by a term within the Hamiltonian and dissipative is via a term in ...
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In Sec. IV of this paper the authors consider the Hamiltonian (Eq. 10) $$H = \omega_a a^\dagger a + \omega_b b^\dagger b - g_0 a^\dagger a (b + b^\dagger)$$ in the regime $\omega_a / \omega_b \... • 1,024 0 votes 0 answers 67 views ### A mechanical system with coupled oscillators and dampers I found here Coupled oscillators, the last one on this page, a system named by the author "Vehicle Suspension System". But I am not sure this modelizes a suspension for a vehicle. I am ... • 113 0 votes 0 answers 58 views ### Pendulum with flexible connecting rod: synchrony in nature Consider a pendulum with a flexible connecting rod. When initializing the free motion, the bob would be released at a position such that the connecting rod is flexed as shown in the figure. There are ... • 2,324 1 vote 1 answer 63 views ### Double eigenfrequencies of normal modes If I have 3 masses displayed along a ring connected by springs, the frequencies I found were: $$\omega^2=\frac{3k}{m},0$$ I don´t understand why I have 2 double eigenfrequencies. Is this possible, if ... 0 votes 1 answer 44 views ### Hamiltonian for closed system describing parametric excitation I am trying to describe a system with parametric excitation. Usually this is described as an open system where the time dependence of a parameter is explicitly included in this differential equation:$...
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Currently working on a problem and I can really figure out how to write the differential equations for it. Here's the situation: So we have a mass $m$ tied to the wall with a spring of constant $k$. ...