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 ...
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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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Physical Interpretation of an Overdamped Pendulum

Consider a damped pendulum whose equation of motion is given in general by $$m\ddot{x}=-\mu\dot{x}-kx$$ where $\mu,k>0$ Rewrite this equation as $$\ddot{x}+2\gamma\dot{x}+\omega^2x=0,$$ where $...
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Is every density moment of a quantum harmonic oscillator a classical harmonic oscillator?

Suppose we have the usual harmonic oscillator: $$ \hat{H}=\frac{\hat{p}^2}{2m}+\frac{1}{2}m\omega^2\hat{x}^2 $$ with an arbitrary initial state. It is well known that the first density moment $\langle\...
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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 ...
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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 ...
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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 ...
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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 ...
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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-...
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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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Hamiltonian of Klein-Gordon Field

The Hamiltonian of the Klein-Gordon Field may be written $$H=\int\frac{d^{3}p}{(2\pi)^{3}}\frac{1}{2\omega_{\mathbf{p}}}\omega_{\mathbf{p}}\left(a^{\dagger}(p)a(p)+\frac{1}{2}(2\pi)^{3}2\omega_{\...
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Difference between Oscillatory motion and vibratory motion

What is the difference between oscillatory motion and vibratory motion. I have read in my book that "If the amplitude of oscillatory motion is extremely small,the motion is called vibratory motion". ...
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Integration over phase space for a one-dimensional harmonic oscillator

The problem asks for a proof of the following equation, and I have no idea on how to approach this: $$\int dx dp \delta(E-\frac{p^2}{2m}-\frac{m \omega^2 x^2}{2})f(E) = \frac{2\pi}{\omega}f(E) ,$$ ...
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What is the force that makes the wave return to its equilibrium point?

The thing is, the force in simple harmonic motion is clear to me. it is the opposite direction of the movement of the object. F=-kx I assume that the force that makes the wave going down is gravity....
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Reconciling Wikipedia and textbook descriptions of ladder operator method #2

I'm trying to reconcile the work in my textbook, Quantum Field Theory and the Standard Model by Schwartz, which I'm finding difficult to follow, with the Wikipedia article for the ladder operator ...
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Quantum Harmonic Oscillator Raising and Lowering operators

The commutator of the operators, $[a,a^\dagger] = 1$ is useful in rewriting the Hamiltonian in a neat way in terms of the creation and annihilation operators. So my question is, Is there a physical ...
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Reconciling Wikipedia and textbook descriptions of ladder operator method

I'm trying to reconcile the work in my textbook, Quantum Field Theory and the Standard Model by Schwartz, which I'm finding difficult to follow, with the Wikipedia article for the ladder operator ...
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Quantum Field Theory: Number Operator $\hat{N} = a^\dagger a$ and bra-ket notation

My textbook, Quantum Field Theory and the Standard Model by Schwartz, says the following: The easiest way to study a quantum harmonic oscillator is with creation and annihilation operators, $a^\...
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135 views

Physical interpretation of time constancy in damped harmonic oscillator

I know that one can mathematically derive and prove that in a damped oscillator (without external driving) the time period of oscillations is a constant. But how can one physically interpret as to why ...
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Energy Eigenvalue for SHO Classical and Quantum

Let's assume we are given a potential for coupled harmonic oscillator: $$U = \frac{k_1(x_1^2 +x_3^2)+k_2 x^2+k_3 (x_1x_2 + x_2x_3)}{2}$$ If I solve the normal modes of the oscillator I get the ...
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Calculate viscous damping coefficient given force

With a force metre I recorded the force vs time of a spring with a disk on the end in water, experiencing viscous damping, during damped oscillatory motion. I pulled the disk to the bottom of the ...
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Step-by-step guide to finding the phase constant in simple harmonic motion

Working on some simple harmonic motion problems involving an oscillating spring/mass system ... the usual. I never really understood exactly how to find the phase constant for the $$x(t)=Acos(wt+phase ...
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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 ...
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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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Lagrangian of a Relativistic Harmonic Oscillator

My Text Book says the Lagrangian for a one-dimensional relativistic harmonic oscillator can be written as $$L = mc^2(1-\gamma) - \frac12kx^2$$ but I've learnt it as; $$L = -mc^2/\gamma - \frac12kx^...
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Mass-Spring system on an accelerating jet

Imagine a perfect mass spring system. If it's put on an accelerating plane, how will the motion change? Is the plane's acceleration like a driving/damping force, where: $$F_{\text{driving}} = \text{...
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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 ...
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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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Projecting energy eigenstates of quantum harmonic oscillator into the coordinate basis

I am trying formally derive the projection of the energy eiegenstates of the 1D quantum harmonic oscillator into the $x$ basis $$ \phi_n(x) = \langle x | n \rangle = \langle x | \frac{{a^{\dagger}}^{n}...
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What is a complex phase shift?

In a complex methods course I am taking, we were given an equation for a particular driven harmonic oscillator where the driving force is trigonometric. I have worked out the math and obtained an ...
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Uniform Circular Motion vs Change in speed of $x$ & $y$ Components

If you are moving at a set rotational speed the x,y components are constantly accelerating and decelerating (aka simple harmonic motion), this is obvious in order to travel in a circular path. My ...
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Kraus operators for two interacting harmonic oscillators: Problem with the calculation (Ex. 8.21 of Nielsen-Chuang)

I'm working with Exercise 8.21 of the Nielsen-Chuang book on quantum information. It illustrates the amplitude-damping quantum channel by the interaction between two harmonic oscillators (the first ...
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Angular velocity vs angular frequency clarification

I can't seem to find a satisfactory answer on stack exchange for this question, so I will present an example which I would appreciate some clarification on. Let's say we have a pendulum with mass $m$ ...
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Uniqueness of quantum ladder for the harmonic oscillator

Context: Griffith's book on Quantum Mechanics (QM), in Section 2.3.1, tries to solve for the stationary states $\psi(x)$ of a harmonic oscillator by solving the Time-Independent Schrodinger Equation (...
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Why are sinusoids so common in nature? [duplicate]

When we are introduced to waves in school, we are often presented with a picture of a sinusoid (or a cosinusoid). Sinusoids can represent the way many physics phenomena behave, still.... Why are ...
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Simple harmonic motion on a vertical spring

Say we have a spring attached vertically to a wall. Now, let's assume that we attach a mass to the spring, but we do not let the spring extend just yet (we could hold the mass on our palm for example)....
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Proving that motion of an $n$ dimensional oscillator can be written as a linear combination of “sine waves”

Here is a related question which might provide some context: LINK. Let's consider an oscillator with equation of motion in $n$ dimensions: $$ \frac{d^2}{dt^2} \vec{x} = K \vec{x}. $$ Given that $\...
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Simple Pendulum in Cartesian Coordinates

Riffing on the question in Simple Pendulum Why Generalized Coordinate Always Angle? , I'm trying to write down Newton's law for a simple pendulum in Cartesian coordinates. (I'm doing this as an ...
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Book recommendations for second quantization

I am trying to familiarize myself with the ideas of second quantization. However, the literature that I can find online seems only to outline the tools of this formalism of quantum mechanics. ...
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Amplitude of Shm if Constant External force is applied

In the attached picture, is the spring mass system in equilibrium with a constant force $F$? My question supposes that the system is slightly displaced from equilibrium (let's say to the left). Is ...
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Intuition behind creation and annihilation operators? [duplicate]

Here I am talking about Harmonic Oscillators with Hamiltonian $$ H=\frac{1}{2m}(p^2+(m\omega x)^2), $$ with eigenstates $|1\rangle,|2\rangle,\ldots$ Many textbooks define the annihilation operator to ...
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Motivation behind action when deriving ''Strings as Harmonic oscillators" in Zwiebach's book on String theory

Page 248 gives us this action and he simply says that we will assume it correct. $$ S=\int d \tau d \sigma ~\mathcal{L}=\frac{1}{4 \pi \alpha^{\prime}} \int d \tau \int_{0}^{\pi} d \sigma\left(\dot{X}...
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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 ...