All Questions
Tagged with harmonic-oscillator or harmonic-oscillator
2,480 questions
4
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What are the maximum spring lengths of a double spring pendulum?
NOT a duplicate of Maximum length stretch of vertical spring with a mass?, I am asking about a system with two connected springs, as shown in this diagram
For a single spring, you can simply equate ...
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vote
0
answers
45
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Time translation invariance of the two-point function
Please refer to this 2023 lecture note by Douglas Ross. In this note, they compute the generating functional for the correlators given by Eq (4.7) for a harmonic oscillator action.
$$\begin{aligned}
&...
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2
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0
answers
40
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Why initial conditions matter while interfering with ongoing SHM of a mass with electric charge and placed in electric field?
The question is related to the situation:
A body of mass M and charge q is connected to a spring of spring constant k. It is oscillating along x-direction about its equilibrium position, taken to be ...
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1
answer
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Approximation to the differential equation $\dfrac{d^2\psi}{d \xi^2} = \xi^2 \psi$ for large values of $\xi$
I'm interested in understanding the approximate solution for large values of $\xi$ (as $\xi \rightarrow \infty$) of the following differential equation
$$\dfrac{d^2\psi}{d \xi^2} = \xi^2 \psi$$
which ...
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2
votes
1
answer
279
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Overlap integral between harmonic oscillators of different shapes
In a diatomic molecule, the nuclear potential in the ground and excited states can take different shapes. The coordinates might be displaced and the curvatures might not be the same. For example, we ...
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0
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43
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Why is this case different from case of simple SHM? [closed]
The question in itself is easy but my doubt is
If we consider a block falling from top to an unstretched spring then it starts performing shm(if the block is connected to the spring). on the bottom ...
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0
votes
2
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244
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Driving force of a mass-spring system
In a horizontal mass-spring system with one spring, an external source supplies a driving force from one end. I know that the force is periodic but I have trouble understanding the direction of the ...
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223
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Kronig-Penney Model $P$ vs $E$ graph
While studying the Kronig-Penney model the author introduced a quantity
$$P=\frac{mVba}{h^2}$$
Where $b$ and $a$ are periodic lengths and $V$ is the potential barrier.
Then he explain the extreme ...
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0
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How to measure the distribution of eigenenergies of a cold atomic cloud in an optical trap?
I have a cloud of cold atoms in an optical trap.
For example a BEC or thermal gas of 87Rb (you can adjust the number from 100 to 10^6) in a harmonic trap created by some far detuned laser.
You want to ...
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2
answers
194
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Why is circular motion "simple harmonic" when there is no restoring force?
While this question seems similar to Is uniform circular motion an SHM, the answers there appear to contradict Berg & Stork (2004).
Berg & Stork first state that simple harmonic motion (SHM) ...
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2
answers
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What is the partition function of a classical harmonic oscillator?
A classical harmonic oscillator has energy given by $\frac{1}{2m}p^2+\frac{1}{2}kx^2$. This means its Boltzmann factor is
$$e^{-\frac{\beta p^2}{2m}}e^{-\frac{\beta k x^2}{2}}$$
where $\vec{x}$ and $\...
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2
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How do you derive the compound pendulum formula? [closed]
How do you derive $$T=2\pi\sqrt{I/mgl},$$ where $I$ is the moment of inertia and $l$ is the length of the pendulum?
Is it even the right formula? How would I derive a compound pendulum formula for a ...
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2
answers
225
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Using Wick's Theorem in an example with the harmonic oscillator [closed]
I understand Wick's theorem to be,
$$T(x)=\mathcal{N}(x)=\sum:\textbf{all contractions}:$$
And I'm researching combinatorics and quantum theory in general.
How would one connect Wicks theorem to the ...
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2
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What sort of coupling of oscillators yields a potential of $\lambda q(t)Q(t)$?
I'm trying to work through Galley's paper, The classical mechanics of non-conservative systems. It starts with a toy problem to demonstrate the need for his full approach. I'm certain understanding ...
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1
answer
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Energy in simple harmonic oscillator in a moving frame of reference
It is pretty straightforward to derive the kinetic energy and the potential energy of a simple harmonic oscillator and to see that they behave like the squares of two sinusoids with a phase difference ...
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3
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2
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Wave amplitude as a complex number?
In section 1-3 An experiment with waves of The Feynman Lectures on Physics (https://www.feynmanlectures.caltech.edu/III_01.html) it says:
"The instantaneous height of the water wave at the ...
0
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2
answers
91
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How to easily prove that operators in the Heisenberg picture have the same expression through other operators? [closed]
I was reading a textbook, and didn't understand this implication. Suppose we have a harmonic oscillator. We know that
$$
a_H = a_S e^{-i\omega t}, a_H^{\dagger} = a_S^{\dagger} e^{i\omega t}
$$
It ...
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5
votes
3
answers
5k
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Correlation function for the ground state of simple harmonic oscillator
I calculated correlation function $C(t)=\langle x(t)x(0)\rangle$ for ground state of Simple Harmonic Oscillator (SHO) in two different methods. But the results do not match.
First Attempt:
From ...
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3
votes
1
answer
95
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Relation beteen harmonic polynomials and spherical harmonics
Considering a spinless particle moving in the 3D space and described by the wavefunction $$\psi(\vec{x})=(x^3+y^3)\frac{e^\frac{-r}{2\lambda}}{r^2}$$ where $\lambda$ is a lengthscale.
I want to know ...
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10
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3
answers
1k
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Quantum harmonic oscillator meaning
Imagine we want to solve the equations
$$
i \hbar \frac{\partial}{\partial t} \left| \Psi \right> = \hat{H}\left| \Psi \right>
$$
where $$\hat{H} = -\frac{\hbar^2}{2m} \frac{\partial^2}{\partial ...
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votes
1
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405
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Using perturbation theory or small oscillation approximation in Harmonic oscillator
Let us assume, we are given the following potential,
$$V(x)=\frac{1}{2}ax^2-2x+\epsilon x^3$$
We need to find the energy levels of a particle bound in this potential
Let us think of the ground level ...
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votes
1
answer
1k
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Cubic perturbation to coupled quantum harmonic oscillators
I recently came across this two-dimensional problem of a particle in a potential of the form
$$V = \displaystyle{\frac{1}{2}m \omega^2} \big(y^2 + x^2y \big) - \alpha y,$$
where $x$ and $y$ are known ...
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0
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522
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Predict the behaviour of this system involving magnets oscillating on springs through connected coils
I came across an interesting problem recently and started to think about the situation in more detail. Here is the setup:
Identical bar magnets are suspended from identical springs, with the North ...
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2
answers
80
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Why is the form of the ladder operators for the QHO what it is?
I'm trying to deepen my understanding of the ladder operators for the quantum harmonic oscillator now that I'm further along in my physics degree, and I can't seem to find anything on why they take ...
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0
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1
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335
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Euler force for pendulum
Hello I have a question related to the Euler force. Why is this force never considered for a simple pendulum?
As far as I understand, Euler force is given by (assume I would consider the 2d pendulum ...
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0
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24
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Why does the EBow work if an electromagnet will pull the string twice per period
I've been thinking about a similar yet not the same idea as the OP of this elderly thread. I don't know how to properly interact with that thread as a obviously do not have an answer nor am I allowed ...
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3
answers
354
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Direction of displacement
Displacement is defined as the vector obtained by joining the final position to the initial position (head towards the final position). Well,i know this is silly but what are these final and initial ...
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1
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Green's Functions
I am having trouble understanding how to apply Green's function to an impulsive forcing function.
I am having trouble understanding how to use Green's function to solve for the motion of a driven ...
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2
answers
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Experiment: pendulum with constant driving force
I just calculated the amplitude of a pendulum for a constant applied force (without friction)
$\left( \frac{\partial^2}{\partial t^2} + \omega^2 \right) x(t) = f(t)$
where $f(t) = F \theta(t)$
The ...
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2
answers
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How to compute classical probability distribution for 1D harmonic oscillator with $K/x$ (central force) potential energy?
I am trying to find, or derive, the probability distribution function for a classical 1D harmonic oscillator with a $K/x$ potential energy (from a $K/x^2$ central force). I am familiar with the ...
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5
answers
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How is an LC oscillator used for generating signals?
I have been trying to understand some practical applications of LC oscillators and I can't seem to find much information available on the net. One consistent application that I see is ...
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1
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223
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Damping constant (damped harmonic motion)
For damped harmonic motion, the equation for the damping force is F=-bv where F is the damping force exerted on the object, v the velocity of the object and b the damping constant.
For an experiment, ...
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3
answers
1k
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Is the quantization of the harmonic oscillator unique?
To put it a little better:
Is there more than one quantum system, which ends up in the classical harmonic oscillator in the classial limit?
I'm specifically, but not only, interested in an ...
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2
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Proof that the one-dimensional simple harmonic oscillator is non-degenerate?
The standard treatment of the one-dimensional quantum simple harmonic oscillator (SHO) using the raising and lowering operators arrives at the countable basis of eigenstates $\{\vert n \rangle\}_{n = ...
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1
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Two answers to one problem, but both seem correct (mathematically) [closed]
The question is:
Two particles are performing SHM along the $x$-axis and about the origin. If the maximum separation between them is equal to their amplitude $A$, find the phase difference.
Method 1-...
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2
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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
$$ \phi_n(x) = \langle x | n \rangle = \langle x | \frac{{a^{\dagger}}^{n}...
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3
answers
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Quantum harmonic oscillators with momentum-position coupling
I have two coupled quantum harmonic oscillators given by the following Hamiltonian:
$$H=\frac{p_{x}^{2}}{2}+\frac{\omega^{2} x^{2}}{2}+\frac{p_{y}^{2}}{2}+\frac{\Omega^{2} y^{2}}{2}+\frac{C p_{x} y}{2}...
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Does $x(t) = a \sin^2(\omega t+c)$ represent a Simple Harmonic Motion or not?
I had a doubt about the equation
$$x(t) = a \sin^2(\omega t+c).$$
Does this equation represent a Simple Harmonic Motion or not?
I did try it myself with 2 methods:
using trigonometry
using the ...
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3
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1
answer
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Why is the resonance frequency of an undamped oscillator equal to the undamped resonance?
I have read this post: 'How do you define the resonance frequency of a forced damped oscillator?'
And I see that the resonant frequency occurs at the undamped oscillation frequency $\omega_0$ as ...
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402
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Driven harmonic oscillator: driving constant force is only temporary
Example: Let $m$ be a point mass that hangs at the equilibrium point $y_0$ on a spring fixed at the end. No damping force acts on the particle. Let $k$ be the spring constant.
If I want to calculate ...
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2
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What is the position as a function of time, after transient, in damped driven harmonic ocillator?
The problem is covered in many books but nowhere I found the answer to this question: wondering what is $x=x(t)$ it looks to me not so trivial because it emerge a sign problem I can't find anywhere. ...
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1
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What is the criterion for oscillatory motion?
A ball bouncing (consider ideal elastic collisions) moves to and from about some point, but there is no equilibrium position. This motion sure is periodic... but is it oscillatory?
What is the ...
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1
answer
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Calculation of normal frequencies of a normal mode
In the Classical mechanics book by Goldstein, it is stated that if one wants to find the normal frequencies of a system, $\omega$ then the following equation has to be solved:
$\left|\hat{V}-\omega^2\...
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1
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Understanding Quantum Harmonic Oscillator with Piecewise Potential [duplicate]
I just got out of an exam today, and have been wrestling with one of the questions.
I was given a simple (quantum) 1D harmonic oscillator, with potential given by:
$${V(x)=\infty, \forall x<0}$$
$$...
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2
votes
1
answer
149
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IMAT 2024 question about a moving pendulum seems to be wrong [closed]
Here is the question from IMAT 2024:
A pendulum rod moves from the vertical position. Which of the
following statements is false?
A) In the absence of friction, the
pendulum tends to come to a stop ...
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votes
1
answer
221
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Exciting a normal mode of $N$ coupled oscillator with driving force
Suppose we have $N$ coupled oscillator with the fixed ends.
We can find the normal modes of this system by considering an infinite system and using space translation symmetry to diagonalize the ...
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1
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1
answer
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Can the equation of total maximum amplitude $A_n=\sqrt{A_1^2+A_2^2+2A_1A_2\cos(\Delta\phi)}$ be used though the waves are not in the same line?
Let $S_1$ and $S_2$ placed in the same point be the source of two waves which are propagating in the same line, also the phase differernce between the two waves $\Delta\phi=0$. Equation of the two ...
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1
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0
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Equations of motion for n-coupled pendulum system
With reference to this article (https://drive.google.com/drive/u/0/mobile/folders/1d-IF8FTyizKHbaHXjVSxfaB3bgciqi4p),
the author uses 2n equations, where n is the number of pendulums, to describe the ...
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3
votes
1
answer
223
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Average energy of an SHM
Why do we usually calculate the average potential or kinetic energy of a simple harmonic motion with respect to time, why not with respect to position?
Why even calculate average energy for an SHM? ...
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3
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3
answers
211
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What actually causes damping in a damped SHM? [duplicate]
We know and have been taught that due to friction on the surface of maybe a spring mass system, the body faces damping. But what is bothering me, is the fact that force due to damping is proportional ...
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