# Questions tagged [anharmonic-oscillators]

Problems concerning oscillators that are not harmonic (i.e. for forces that are not linearly proportional to position).

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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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### What is the simplest PDE/ODE/model I can use to understand how nonlinearities can lead to leakage of energy to higher harmonics in an oscillator?

I came across this problem in the study of surface waves in an oscillating cylindrical vessel of liquid. There are various eigenmodes described using Bessel functions, and energy transfer can happen ...
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1 vote
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### Why is synchronisation only possible for self-sustaining oscillators

A self sustained oscillator is any oscillator which obeys the following 3 key properties (Balanov 2009): They do not damp They are capable of oscillating without being driven by an external force. ...
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### Calculate period time from potential energy [duplicate]

The question asks: The potential energy of a particle in one dimensional space is: $$U = \frac{1}{2}Ax^2 + \frac{1}{4}Bx^4$$ I need to calculate the period time, from the period calculate the ...
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### Parametric Resonance Analysis using Perturbative approach

I'm reading Parametric Resonance from Landau's Mechanics Text. A similar calculation is done here. Supposing a parametric oscillator given by $$\ddot{x}(t)+\omega_0^2(1+h\cos(\gamma t))x(t)=0$$ It's ...
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### Analysis of damper having mass

How to do analysis of a non ideal viscous damper (damper having mass)? How to find out an equivalent system for it?(having a ideal damper)
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### What are quantum anharmonic oscillators?

I have just started studying about quantum computers (hardware side) and I am really confused about what is a quantum anharmonic oscillator. I have read somewhere that a qubit is the physical ...
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### Deriving a model of a point-driven Chladni plate

Please note — this question considers a point-driven Chladni plate, not Chladni's classical experiment. I'm aware of various other questions concerning the latter here on Physics.SE. As the title ...
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### Divergent Energies and Analytical Continuation - Two questions on the inverted harmonic oscillator and the inverted double well

I have two questions on the general topic of energy potentials that diverge at infinity. First of all, the inverted harmonic oscillator. I found this post on Physics SE, Inverted Harmonic oscillator. ...
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### Approximating the energy levels of the anharmonic oscillator using WKB

I got stuck trying to solve this problem: Given the potential $$V(x) = \frac{m\omega^2x^2}{2}-\beta x^4,\ \beta>0$$ I need to evaluate the deviation of the energy levels from the harmonic ...
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### Ladder Operators for a nonlinear oscillator

I was wondering if there was a way to construct the ladder operators for a nonlinear oscillator given by the Hamiltonian $$H=x^2+p^2+\lambda x^4$$ If we were to just calculate scattering amplitudes, ...
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### A question about derivation of the potential energy around the stable equilibrium point

I'm learning about harmonic oscillators. In the last lecture my teacher derived the potential energy of a system that has a stable equilibrium point but not a harmonic oscillator. At the beginning of ...
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### Is it possible for a motion to be isochronous (time period is independent of amplitude) but not true s.h.m.? Can an s.h.m. be non-isochronous?

Is it possible for a motion to be isochronous (time period is independent of amplitude) but not true simple harmonic motion? Can a simple harmonic motion be non-isochronous? Another question I have is ...
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### Meaning of "harmonic"

I'm trying to understand the meaning of the term "harmonic". IE, appearing in following sentence of Fluctuation-dissipation relations for stochastic gradient descent The second relation (...
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### How is a quartic oscillator solved in classical mechanics?

Quantum mechanically, a quartic anharmonic oscillator with potential $$V(x)=\frac{1}{2}m\omega^2x^2+\lambda x^4$$ is dealt with perturbation theory- the approximate energies $E_n$ and energy ...
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### First-order correction to energy in perturbed harmonic oscillator [closed]

I know, from the perturbation theory, that, if I have the hamiltonian $$\hat H = \hat H_0 + \lambda \hat W$$ where $\hat H_0$ is the unperturbed hamiltonian of which I know its eigenvectors and ...
The question: A particle of mass $m$ is executing oscillation on the $x$-axis. Its potential energy is $U(x)= K|x|^3$, where $K$ is a positive constant. If the amplitude of oscillations is $a$, ...