# Questions tagged [harmonic-oscillator]

The term "harmonic oscillator" is used to describe any system with a "linear" restoring force that tends to return the system to an equilibrium state. There is both a classical harmonic oscillator and a quantum harmonic oscillator. Both are used to as toy problems that describe many physical systems.

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### Extracting solution from driven SHM

I guess maybe I should rather ask at the math stack exchange? I have a simple harmonic undamped oscillator driven by a cosinusoidal force: $$\ddot{x}+\omega_o^2x=f\cos(\Omega t).$$ I've managed to ...
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### Factors effecting amplitude of damped spring

Let say we have a spring under simple harmonic motion. What are the independent variables that effect the time taken to reach half the initial amplitude during damping? I am guessing a few would be ...
2answers
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### The effect of tension force on a pendulum swinging in simple harmonic motion

In physics class, I learned that the reason a pendulum moves about the equilibrium position is due to the force acting towards the center, which is the resultant force of tension and weight. However,...
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### Ground state of two electrons in one dimensional S.H.O

Let's assume I have a one dimensional harmonic oscillator. The eigenvalue of the oscillator would be $E= (n+ \frac{1}{2}) \hbar \omega$. Now I have two electrons (their spins are identical, I mean ...
2answers
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### What is the (triplet) eigenstate for two electrons? [duplicate]

Let's assume I have a harmonic oscillator which is one dimensional. What is my plan is to work the the two electron's spin states and my requirement is that they have to be in the triplet sates. Lets ...
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### Find the maximum amplitude of oscillation of the spring mass system [closed]

A platform of mass m is supported by a spring of force constant k as shown. When the platform is slightly pressed and released, it performs simple harmonic motion. Find the maximum amplitude of ...
1answer
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### Triangle swinging around a pivot

im studying oscilatory motion, and i have a problem that asks me for the angular frequency of a group of sticks,each stick has mass M and length L, that form an equilateral triangle swinging around a ...
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### Manev potencial and some problems with it [on hold]

Given the Manev potential by the equation below $$\ V_M(r) = - \frac{-mMG}{r} \left(1 + \frac{\gamma MG}{c^2r}\right)$$ in which: M is the Sun's mass; m is the planet's mass; G is Newton's ...
1answer
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### Coupled oscillators in Hamiltonian formalism - problem with diagonalization

I have a problem with simple coupled oscillator system. I tried to solve single oscillator with Hamiltonian, and then coupled system of two, but when I try to put coupling constant $k^\prime=0$ in my ...
1answer
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### Damping coefficient and damping ratio

I am not sure if I understand the term damping coefficient correctly (I am a high-school student). Here's the link for the info that I learned: http://hyperphysics.phy-astr.gsu.edu/hbase/oscda.html ...
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### Central force fields [closed]

A particle of mass m moves In a central force field given in magnitude by f(r)= -Kr, where k is a positive constant,if the particle starts at r=a,theta=0, with a speed v in a direction perpendicular ...
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### Experimental time-series for quantum particle-in-a-box or simple harmonic oscillator?

I would like to see experimental results for repeated measurement of a single-particle, quantum system that is approximately either particle-in-a-box or simple harmonic oscillator. If particle-in-a-...
1answer
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### Energy Conservation of waves at a boundary

Consider a wave traveling on a string with velocity $\upsilon$ and mass density $\rho$ having unit length so that the mass of the string is $\rho$. Considering the string to be a simple harmonic ...
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### 3D harmonic oscillator magic numbers

I know that, $$V(r) = (1/2) m \omega^2 r^2 ,$$ $$\omega \approx 40(Z+N)^{-1/3}\ \rm{MeV}$$ and $$E = (n+3/2) \hbar \omega.$$ How do you find the magic numbers of protons and neutrons which ...
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### Why does light come as quanta of the harmonic oscillator?

I've recently been learning the basics of Quantum optics and it seems to be a fundamental concept that light is best described in the framework of the Quantum Harmonic Oscillator. This lead to a ...
3answers
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### In what sense is a quantum field an infinite set of harmonic oscillators?

In what sense is a quantum field an infinite set of harmonic oscillators, one at each space-time point? When is it useful to think of a quantum field this way? The book I'm reading now, QFT by ...
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### Equivalency of $Q$ Factor Definitions

The Q factor is defined (seemingly) as $$Q=2\pi\frac{\mathrm{energy \, \, stored}}{\mathrm{energy \, \,dissipated \, \, per \, \, cycle}}$$ however on Wikipedia is says that the Q factor can be ...
1answer
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### Spring constant of tuning fork

I was playing with a tuning fork and got to wondering how to find it's spring constant (assuming damped oscillation). I can find plenty of resources about materials for springs, but not a whole lot ...
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### Multiplicity Identity in Kittel's Thermal Physics

On page 25 of Kittel's Thermal Physics, the author derives the multiplicity of $N$ harmonic oscillators with total quanta of energy $n$, $g(N,n)$. He writes \begin{align} g(N,n) &= \lim_{t\...
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### Oscillating spring, speed close to the equilibrium: How is this answer not 1.5? [closed]

I have this question with the answer listed as $2.0\,\mathrm{m/s}$. "A $1.25\,\mathrm{kg}$ mass on a spring with a constant of $12.0\,\mathrm{N/m}$ is oscillating back and forth. Its maximum ...