# 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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### Anharmonic oscilator without friction

Hello, everyone Me with my friend do a project on physics in the university. We want to describe the non-harmonic oscilator, so we built the system shown in the picture. The problem is there is a ...
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### What is the next higher order correction to Hooke's Law for a typical steel spring?

Near equilibrium the potential of a typical steel spring is well approximated by a quadratic function. I'm having trouble finding a reference for the what is the next-to-leading order contribution, ...
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### Anharmonic field theory: pedagogical simplifications

Thank you all for so much help as I work through Zee's QFT book. Here I finally have a question about physics instead of math. Zee makes several comments that the main thing left to do in QFT is find ...
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### Hooke's full unapproximated law

It is known that the Hooke's law relating the restoring force of a spring to the distance of retraction from the equilibrium position, is only an approximation. That is, the equation $F=-kx$ is only ...
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### Simple pendulm motion for larger angular displacement? [duplicate]

What will be the nature of the motion of a simple pendulum for larger angular displacement? Will that be a periodic motion? If so, will the time period increase or decrease?
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### A small error in Landau & Lifschitz “Mechanics” (3rd ed.)?

I think I found a small error in Landau & Lifschitz "Mechanics" (3rd ed.). In section 28 (Anharmonic oscillations), they are discussing how to solve the following anharmonic oscillator problem: ...
144 views

The pendulum equation states that the time period $T=2π\sqrt{l/g}$. This is based on the small angle approximation where we approximate l $$\frac{{\rm d}^2 θ}{{\rm d}t^2 }= -\frac{g}{l}\sin θ \... 3answers 7k views ### Does amplitude affect time period for spring mass system? I know that with the formula T=2\pi\sqrt{\frac{m}{k}} the time period is not related to the amplitude. However, would amplitude matter if i do this experiment in real life. Would a greater amplitude ... 0answers 69 views ### How to write classical Hamiltonian H = \frac{I^{2}}{2} in (p,q) variables? Suppose I have a completely integrable 1 degree of freedom Hamiltonian H(I, \varphi) = \frac{I^{2}}{2} written in action-angle variables (I, \varphi) \in \mathbb{R} \times \mathbb{S}. What ... 0answers 97 views ### Papers/books with theoretical data on anharmonic oscillators I am trying to solve an-harmonic oscillator (with x^4 terms) and need theoretical data to compare with my numerical data. I have searched research papers on anharmonic oscillators and few ... 2answers 367 views ### Can there exist harmonic oscillator with asymmetric coupling? In Classical Mechanics textbooks usually, for a coupled harmonic oscillator with two masses, coupling is taken to be same in both directions (i.e coupling constant w.r.t to m1 is same as that with ... 1answer 87 views ### Why does harmonic oscillation propagate better? I read that EM radiation can propagate forever only if it follows the harmonic pattern. If that is true, can you explain why? Why doesn't a different oscillation propagate forever? What happens: is ... 3answers 6k views ### Why does a simple pendulum or a spring-mass system show simple harmonic motion only for small amplitudes? I've been taught that in a simple pendulum, for small x, \sin x \approx x. We then derive the formula for the time period of the pendulum. But I still don't understand the Physics behind it. Also, ... 1answer 531 views ### QM anharmonic oscillator - Feynman diagrams, calculating free energy I have the quantum anharmonic oscillator:$$H = \frac{\hat{p}^2}{2m} + \frac{1}{2}m\omega^2 \hat{x}^2 + \frac{\lambda}{4!}\hat{x}^4$$and I want to find the free energy (so essentially \log Z(\beta)... 1answer 245 views ### How to solve the 10000th eigenvalue of the anharmonic oscillator? Given a certain Hamiltonian, for example,$$ H = -\frac{1}{2}\frac{\partial^2}{\partial x^2 } + x^4 . $$, what methods can we use to approximate the nth eigenvalue, for very large n? For ... 1answer 588 views ### Can quartic oscillator's energy eigenvalue, i.e. (0+1)-dim \phi^4 theory, be solved exactly? For a potential of anharmonic oscillator like this:$$V= \frac{1}{2}m \omega^2 x^2+\frac{\lambda}{4}x^4$$Can eigenfunction and eigenvalue of Hamiltonian be solved non-perturbatively that is ... 1answer 349 views ### Using perturbation theory to solve classical anharmonic oscillations A point mass m is allowed to move in the x-y plane. Given k, a to be the spring constant and springs' natural length respectively. The springs are parallel to the x axis. \hskip2in ... 1answer 627 views ### Scaling the Time Independent Schrodinger Equation What seems like a rather simple question is causing me a lot of difficulty as my base in mathematics is weak. I want to know how I would scale the Schrodinger equation to find dependence on mass, m,... 1answer 1k views ### Finding Energy Eigenvalues of Simple Harmonic Oscillator for Higher Order Potentials I am trying to find energy eigenvalues for a particle in a potential \ V(x) = Bx^\gamma where \gamma is a positive, even integer (2,4,6,8....). Considering boundary conditions, V(x) will go to ... 1answer 384 views ### The actual period of a pendulum at 90°. Looking for the correct formula Do you have access to any scientific experiment which gives the period of a pendulum when the angle is 90^\circ: this article says T varies to about 18\% up to 90^\circ, so for a seconds ... 0answers 324 views ### Anharmonic oscillator on quantum mechanics I'm studying the following Hamiltonian for an anharmonic oscillator in quantum mechanics: \begin{equation} \hat{H} = \frac{1}{2 m} \left( \hat{\vec{p}} - \frac{e}{c} \hat{\vec{A}} \right) + \frac{ m \... 0answers 270 views ### Anharmonic quantum oscillator with momentum perturbation Given the following quantum oscillator for a particle with mass m, and perturbation -\gamma P (\gamma is a constant):$$H=\frac{P^2}{2m}+\frac{1}{2}m\omega^2X^2-\gamma P One could find the ...
The differential equation that gives the equation of motion of a pendulum where: $m$ is the mass $L$ is the distance between the pivot and the body's centre of mass $g$ is the acceleration due to ...