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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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Cubic 1st-order Lagrangian for nonlinear harmonic oscillation [closed]

I am considering the nonlinear oscillators and dedcide to work for the higher order form. And some books writes the 3rd order of Lagrangian of the nonlinear harmonic oscillator in this way: $$L=\frac{...
Shihchia's user avatar
2 votes
1 answer
87 views

How to compute the vector field from a potential in the complex plane?

I am watching this Youtube video and I have the following dumb question around 1:18:00: How do you draw the vector field for a given potential in the complex plane? He gives the potential $V(x) = x^4-...
Wyatt Kuehster's user avatar
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0 answers
27 views

Robustness to noise of a parametric oscillator

I'm an experimentalist working with trapped nanoparticles with optical dipole trap experiments. In the experiment, surprisingly I observed that if I periodically modulate (at full depth) the trap ...
Some random physicist's user avatar
1 vote
2 answers
48 views

Period of the pendulum (realistic) is shortening in time?

I am doing an experiment with a pendulum and am trying to measure its period over time. I built myself a contraption that uses a 3D printed pendulum with a weight attached at the end. For this ...
Patrik Kokinda's user avatar
2 votes
4 answers
746 views

Why is Simple Pendulum not SHM?

Why does Simple pendulum's motion not hold as SHM for large angles, only for small angle approximations? The restoring force is still directed towards the mean position. I know mathematically the ...
High School Student's user avatar
2 votes
3 answers
385 views

Dynamics of a mass-spring system with non-ideal spring

Show that a mass attached to a non ideal spring that has a restoring force given by $-kx-ax^3$, where $x$ is the displacement from the equilibrium position, executes a periodic motion. What's the ...
Lucas Rodrigo's user avatar
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1 answer
86 views

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 (...
YoussefMabrouk's user avatar
2 votes
1 answer
168 views

Solving differential equation in perturbation theory

The differential equation of an anharmonic Oscillator with Newtonian friction is $$ \ddot{x}+\varepsilon \dot{x}^2+x=0 .$$ The initial conditions of the System are $$ \begin{align*} x(0)&=1\\ \...
Jowo's user avatar
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2 votes
1 answer
113 views

Anharmonic effects in crystals, help with intuition

I've been reading a bit about how it is necessary to consider anharmonic effects in crystals if one wants to properly understand things like thermal expansion etc. So for example here: So the cubic ...
JPP's user avatar
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1 vote
0 answers
97 views

Perturbation to two-point correlation function for the anharmonic oscillator [closed]

I am trying to answer a question regarding the computation of the first-order correction to the two-point correlation function for the anharmonic oscillator with Lagrangian: $$ L = \frac{m}{2} \dot x^...
Noud van Halteren's user avatar
3 votes
1 answer
88 views

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 ...
Chillpadde's user avatar
2 votes
1 answer
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Perturbative expansion of energy eigenstates [duplicate]

If we add quartic term in quantum harmonic oscillator, $$V(x)=\frac{mx^2}{2}+\frac{m^{2}\omega^{3}}{\hbar}\hat{x}^{4}.$$ $$H(\lambda)\,=\,H^{(0)}+\lambda\,\frac{m^{2}\omega^{3}}{\hbar}\dot{x}^{4}\,=\,...
Iti's user avatar
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2 votes
1 answer
109 views

Nonlinear PDE from Chain of Oscillators

Some years ago, I was reviewing the calculation for the dynamics of limiting case for a chain of springs with transverse oscillations and found a partial differential equation for which I haven't been ...
motherboard's user avatar
5 votes
2 answers
922 views

Rigorously prove the period of small oscillations by directly integrating

This answer proved that $$\lim_{E\to E_0}2\int_{x_1}^{x_2}\frac{\mathrm dx}{\sqrt{2\left(E-U\!\left(x\right)\right)}}=\frac{2\pi}{\sqrt{U''\!\left(x_0\right)}},$$ where $E_0:=U\!\left(x_0\right)$ is a ...
Ulysses Zhan's user avatar
2 votes
2 answers
334 views

Why is the bending mode of carbon dioxide harmonic?

Here's a simple classical model of a carbon dioxide molecule: This gif illustrates the "bending mode" vibration. If the carbon atom moves a small distance $\mathrm{d}x,$ then the springs' ...
Mark Eichenlaub's user avatar
0 votes
2 answers
66 views

Trying to prove chaotic motion from the equation of a nonlinear oscillation [closed]

So I'm given the equation of a nonlinear oscillation: $x''+ω_0^2x=λx^3$ Assume that $x_1$ and $x_2$ are solutions to the differential equation above. Therefore; $x = αx_1+βx_2$ $x' = αx_1'+βx_2'$ $x'' ...
mEXsACHINE's user avatar
2 votes
4 answers
585 views

Does classical simple harmonic motion violate thermodynamics?

If SHM allows for motion to occur forever, we can consider it perpetual motion, does this imply that the second law of thermodynamics is violated? Or does the presence of an external force act on the ...
user1007028's user avatar
1 vote
0 answers
92 views

Integral partition function of a cubic anharmonic oscillator Energy complex values [closed]

I am interesting in the following integral $$\int_{-\infty }^{\infty } e^{-\frac{g z^3}{6}-\frac{z^2}{2}} \, dz.$$ Mathematica does not provide any result nor maple either I try to used$$ \text{...
Charlessilva's user avatar
1 vote
1 answer
132 views

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. ...
Vishal Jain's user avatar
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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 ...
Alon's user avatar
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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 ...
Young Kindaichi's user avatar
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1 answer
59 views

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)
Heisenberg's user avatar
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1 answer
888 views

How to solve SHM questions using Taylor's Series? [closed]

Q) A point particle is acted upon by a restoring force $-kx^3$. The time period of oscillation is $T$, when the amplitude is $A$. The time period for an amplitude $2A$ will be (A) $T$ (B) $T/2$ (C) $...
Harsh Darji's user avatar
1 vote
0 answers
44 views

Solution of a polynomial boson problem

I was reading about anharmonicity that can be added to the harmonic oscillator model and I got myself wondering whether it is possible and whether there is a general method to solve (I mean ...
Yepman's user avatar
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1 answer
130 views

Why is a phase shift through a time delay not used for damping in vibration dampers?

Why do oscillation dampers use signal conversion through a sufficiently massive electrical circuit (with resistors, capacitors, diodes) to create antiphase, instead of simply shifting the signal in ...
Dashwind's user avatar
0 votes
2 answers
312 views

Decreased period of pendulum

I'm doing an experiment with a physical pendulum and as time passes, the time taken for n cycles is shorter than would be predicted from the period (i.e. the time taken for the first n cycles is less ...
planckton's user avatar
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1 vote
0 answers
145 views

Poincare section for the duffing Oscillator

I have used the 4th Order Runge-Kutta method in order to estimate the values in which the Duffing Oscillator is chaotic. According to Wikipedia, the Duffing Oscillator is chaotic for values of $\alpha$...
James's user avatar
  • 11
3 votes
4 answers
250 views

Asymptotic frequency of nonlinear oscillator $\ddot x = -x-{\dot x}^3$ (speed cubed)

A particle oscillates according to the equation $\ddot x = -x-{\dot x}^3.$ The positive positions of the particle when it changes direction, $\dot x = 0$, are $x_1,x_2,\ldots$. I want to show that $$\...
Pachirisu's user avatar
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1 answer
148 views

Equations of the spherical pendulum in different coordinates [closed]

I am trying to derive the equations of motion of a spherical pendulum, but instead of using the angles of the spherical coordinate system $\theta$ and $\varphi$, I want to use the angles $\alpha$ and $...
user655870's user avatar
1 vote
0 answers
133 views

Solve nonlinear, forced and damped Duffing oscillator

I am trying to solve a Duffing type equation by using Van Der Paul's method: \begin{align} \ddot{x} + \omega^2 x + 2 \gamma \dot{x} + \beta x^3 = f \cos(\Omega t) \end{align} with $$x(t) = Re[A(t) \...
Andrew Semyonov's user avatar
0 votes
1 answer
134 views

Differential equation for the anharmonic oscillator

In my project me and my partner used the engine to constrain the system so we can see the anharmonic oscillations. In our first analysis we get only odd powers in differential equation, so there ...
Eyal Bass's user avatar
4 votes
1 answer
747 views

Why is a kalimba note anharmonic?

I play a kalimba, and have also recently written a toy program that helps me tune it using a "naively applied FFT" without any sophisticated DSP. The Nyquist frequency is 24 kHz. The kalimba ...
Reinderien's user avatar
4 votes
0 answers
104 views

Compute probability current from WKB approximation

I struggle to reproduce a calculation from the Appendix of the paper "Anharmonic Oscillator: A Study of Perturbation Theory in Large Order", Physical Review D, 7 (6) 1973, link to abstract. ...
Smerdjakov's user avatar
3 votes
1 answer
114 views

Anharmonic oscillator without friction

My friend and I are doing a project on physics at the university. We want to describe the non-harmonic oscillator, so we built the system shown in the picture. The problem is there is friction between ...
Eyal Bass's user avatar
1 vote
0 answers
170 views

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, ...
user1247's user avatar
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0 votes
1 answer
73 views

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 ...
hodop smith's user avatar
1 vote
1 answer
272 views

Landau-Lifshitz skips a step in anharmonic oscillations

In chapter 28 of Landau-Lifshitz Classical Mechanics textbook they try to explain how to get the motion of a particle with the Lagrangian: $L=\frac{1}{2}m\dot{x}^{2}-\frac{1}{2}m w_{0}^{2}x^{2}-\frac{...
Cast fj's user avatar
  • 15
3 votes
2 answers
4k views

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 ...
mevis's user avatar
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2 votes
0 answers
286 views

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 ...
Ailurus's user avatar
  • 71
5 votes
1 answer
285 views

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. ...
Smerdjakov's user avatar
0 votes
2 answers
404 views

Approximating the energy levels of the anharmonic oscillator using WKB [closed]

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 ...
LLM's user avatar
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5 votes
1 answer
418 views

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, ...
adithya's user avatar
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5 votes
4 answers
2k views

How to obtain large order perturbation series for cubic anharmonic oscillator?

Consider the potential $$V(x)= \frac{x^2}{2} + gx^3.\tag{1}$$ Then the time-independent Schrödinger equation becomes $$\left(-\frac{1}{2}\frac{d^2}{dx^2} + \frac{x^2}{2} + gx^3 \right)\psi = E(g) \psi....
Paranoid's user avatar
  • 427
0 votes
1 answer
282 views

Time period of an anharmonic but periodic motion [closed]

How do I find the time period of anharmonic motion given an expression of force as a function of $x$? This is the question I was solving: $$ U(x)=k|x|^3 $$ where $k$ is a positive constant. If the ...
Vamsi Krishna's user avatar
0 votes
0 answers
60 views

Why it is not possible to get exact solution for cubic potential perturbation for 1D SHO and we have to use perturbation theory? [duplicate]

Can anyone help me in providing the process of finding exact solution in case of cubic perturbation in 1D SHO, or any suitable resource?
RISHAV SAGAR's user avatar
5 votes
3 answers
1k views

Why is the ground state energy of a linearly perturbed quantum oscillator always lower than its harmonic counterpart?

I am concerned with a QHO that is linearly perturbed in $x$, i.e. $$ H = \hbar \omega \left(\hat{n} + \frac{1}{2}\right) + \lambda \underbrace{\left(\hat{b}+ \hat{b}^\dagger \right)}_{\propto \hat{x}}....
MrArsGravis's user avatar
0 votes
1 answer
150 views

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 ...
M. Çağlar TUFAN's user avatar
0 votes
1 answer
273 views

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 ...
Pierre Euler's user avatar
2 votes
1 answer
85 views

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 (...
Yaroslav Bulatov's user avatar
2 votes
1 answer
2k views

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 ...
Solidification's user avatar