The term "harmonic oscillator" is used to describe any system with a "linear" restoring force that tends to return the system to a 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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Initial conditions for shm [closed]

This is the part of the question from the book that I am studying, "A mass of $0.75\:\mathrm{kg}$ is attached to one end of a horizontal spring of spring constant of $400\:\mathrm{N m^{−1}}$. The ...
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137 views

How to find frequency with only amplitude? [closed]

I came across the following problem earlier. A platform oscillates in the vertical direction with simple harmonic motion. It’s amplitude of oscillation is C. What is the range of frequency of ...
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63 views

Oscillating Ruler

I was bored in the office and stuck a ruler in my desk and started maing it oscillate. I noticed that when I looked at it from the top, there were some bands of color I observed (as in the pic below) ...
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Energy of driven dampened oscillator

Given the oscillator described by: $$m\ddot{x}+\gamma \dot{x}+kx=F_0\cos(\omega t)$$ And supposing the system is at it's stable state, I wish to calculate the following: 1) The system's energy at any ...
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Simple harmonic motion, maximum kinetic energy [closed]

Why kinetic energy is maximum at mean position?
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How to apply cutoff in path integral?

I am working on harmonic oscillator for quantum fluctuations (apart from clasical part), path may written as $$ S_q=\int_0^Tdt[(\partial_tq)^2+w^2q^2] $$ This may written as $$ S_q=\int dt(q\Delta q) ...
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59 views

Excitation source in 2D grid coupled harmonic oscillator

In A. Zee's Quantum field theory in a Nutshell, he describes the QFT analogy of a matress, a 2D grid of points $q_a$ connected by springs (first page of first chapter, $q_a$ is the vertical ...
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122 views

Motion of Thompson's jumping ring

Thompson's jumping ring experiment is set up as follows: There is a force acting on the ring $F(x)$ where $x$ is the vertical displacement. The force is due to the $90^\circ$ out of phase flux ...
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615 views

Pendulum's motion is simple harmonic motion

For a pendulum's motion to be simple harmonic motion (S.H.M.) is it necessary for a pendulum to have small amplitude or S.H.M. can be produced at large amplitudes as well? If it is really necessary ...
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Proportionality of states in quantum harmonic oscillator

What is the justification for $a_{\pm} \psi_{n}$ being proportional to $\psi_{n\pm1}$ in a quantum harmonic oscillator? Here $a_{\pm}$ is the raising/lowering ladder operator.
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Solution to Harmonic Oscillator

The damped oscillator is governed by the equation of motion: $\ddot{x} + 2\beta \dot{x}+\omega _{0}^2x=0$ where $\omega _{0}=\beta$ for an oscillator with critical damping. The solution is $x(t)= e^{-\...
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60 views

Driven harmonic oscillator problem : change of variables and expressing the extension of the spring

I'm struggling to understand the reasoning in question $b)$. Basically, I had to write Newton's Second Law and do a change of variables to put the equation of motion of a mass $m$ in a specific form, ...
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301 views

Spring-block system, simple harmonic motion, time period

In the case of simple harmonic motion of spring block system, why time period of the simple harmonic motion of the block is independent of acceleration of the system (spring-block system)?
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Calculating trajectory of particle moving in a potential (SHM)

I have been given the potential of a simple harmonic oscillator: $$V=\frac{1}{2}kx^{2}$$ I want to calculate the value $x(t)$ of a particle moving in this potential, with initial conditions $x(t=0)=...
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74 views

Response functions for the quantum harmonic oscillator

I'm going through problems in Quantum Field Theory for the Gifted Amateur, and have been trying to understand a problem on the forced quantum oscillator [$L = \frac{1}{2}\dot{x}(t)^2-\frac{1}{2}m\...
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Derive an equation related to magnetism [closed]

Solve the equations for $v_x$ and $v_y$ : $$m\frac{d({v_x)}}{dt} = qv_yB \qquad m\frac{d{(v_y)}}{dt} = -qv_xB$$ by differentiating them with respect to time to obtain two equations of the form: $$...
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Simulation of oscillator with frequency dependent damping

What would be the equation for the frequency dependent damping of harmonic oscillator? Is there something like: $$ \ddot{x}+2\delta\dot{x}+\omega_0^2x = \frac{F}{m}f(t) $$ with frequency dependent ...
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1answer
139 views

Probability current for electron in uniform magnetic field: wave function forever splitting apart?

In this document http://hitoshi.berkeley.edu/221a/landau.pdf on Landau levels, in section 4, page 19, "Transitionally invariant Gauge", they analyze the free electron in a uniform magnetic field ...
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214 views

Area of phase space of Harmonic oscillator

We all know that the phase trajectory of an undamped linear harmonic oscillator is an ellipse. But when we calculate the area of the ellipse we find it does not depend of mass of the particle. Why is ...
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Quantum harmonic oscillator - Where am I going wrong?

Find the relationship between $a_+\psi_n$ and $\psi_{n+1}$ My attempt: I was able to prove that $\int{(a_+\psi)^*(a_+\psi)dx} = \int{\psi^*({a_-a_+\psi})dx}\qquad\qquad (1)$ And, $(a_-a_+-\...
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101 views

Number of states in a given Landau level

For an electron in a uniform magnetic field, in free space, we seek to find the number of allowed states in a given rectangle $L_x L_y$ (for some fixed Landau level). In effect we are tiling 2-D ...
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$N$ coupled quantum harmonic oscillators

I want to find the wave functions of $N$ coupled quantum harmonic oscillators having the following hamiltonian: \begin{eqnarray} H &=& \sum_{i=1}^N \left(\frac{p^2_i}{2m_i} + \frac{1}{2}m_i\...
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124 views

Density of states of classical harmonic oscillator in phase space

Since all classical harmonic oscillators are ellipses in phase (position-momentum) space, and since the entire phase trajectory of a given system (with a fixed rigidity and mass factor) can be ...
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State time evolution of a quantum harmonic oscillator with a Dirac-Delta function as an initial state [closed]

I have a question just like this Phys.SE problem here with a difference that our system is a harmonic oscillator (rather than a free particle). A particle with mass $m$ is connected to a string with ...
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Why would the relationship between period and mass be important to you in a Simple Harmonic motion?

My lab's teacher always asks us why we're there at lab before the class starts. We already know the variables we're supposed to measure, so we frequently say (We used to say): "We want to find out the ...
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Would the system exhibit periodic motion? [closed]

A mass moving in one dimension has a potential energy given by :- $$V(x)=\frac{k_1}{2}x^2+\frac{k_{2}}{x}$$ where $k_1$ and $k_2$ are positive constants and $x>0$. Is this system exhibiting ...
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Zero-point energy amplitude calculation

On this page https://www.miniphysics.com/simple-harmonic-oscillator.html It is stated that for a linear restoring force of $F = -k \Delta x$, the total energy is $ E = K + U $ or rather $ \\ E = \...
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Where does this period formula come from?

I extend a warm greeting to all of you. I just carried out a simple harmonic motion experience at lab. We're told to find out the relationship between Period and Mass. That thing is I've always found ...
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162 views

Harmonic Oscillator propagator

I'm reading the book on Quantum Field Theory by Anthony Duncan, and I'm a little lost with something of propagators. He first define the propagator $K(q_f,T;q_i,0)$ as the amplitude of detecting a ...
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97 views

If electromagnetic waves can be generated by oscillation of a coil why can't light? [duplicate]

I was recently reading how electromagnetic waves are generated using oscillation of a current in an antenna. Why is it that this principle cannot be used to generate light?
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111 views

Retarded Quantum Harmonic Oscillator

Suppose there is a harmonic oscillator and at some time acts on him a force. The external force $F (t)$ being zero before $t = 0$ and after $t = T$ . The oscillator was in its ground state for all ...
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Average energy of a damped-forced harmonic oscillator during a period t

In my textbook, it's stated without proving the following identity for a classical damped-forced harmonic oscillator: $$ \bar{E}^t = \bar{T}^t + \bar{V}^t = 2 \bar{T}^t \, , $$ which states that ...
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Why doesn't the coupling spring provide restoring force in longitudinal oscillation of two masses?

I was reading longitudinal oscillations of two masses from Crawford's Waves. The displacement of $m_1$ is given by $\psi_a$ & that of $m_2$ is given by $\psi_b$. The differential equations ...
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Classical probability of harmonic oscillator

I am trying to derive the classical probability density function to find the harmonic oscillator at position $x$. I am confused between the random variables involved here $x, t$ and not able to ...
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Books on waves with Fourier Transforms [duplicate]

There are many waves and oscillations books out there that also include Fourier analysis but very few give the subject a thorough treatment, they just pass it in a few pages. If anybody has any ...
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Spring-mass system with variable stifness $m \ddot{x}+k(x)x=0$, time period is known, stifness is unknown

This question is somewhat related to my previous question: What is the time period of an oscillator with varying spring constant? In that question, time period of mass-spring system with variable ...
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Why is the wave equation so pervasive?

The homogenous wave equation can be expressed in covariant form as $$ \Box^2 \varphi = 0 $$ where $\Box^2$ is the D'Alembert operator and $\varphi$ is some physical field. The acoustic wave ...
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Conventionally, how many amplitudes does a (harmonic) oscillator pass through in one full cycle? [closed]

I don't know the typical scientific convention. My book says there are 4 amplitude. But no matter where I start the oscillator , the answer is at most 3.
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Harmonic oscillator ensemble

Suppose we have an ensemble of classical 1D harmonic oscillators, with displacement $x = A \cos(\omega t+\phi)$, where the phase angle $\phi$ is equally likely to be any angle between $0$ and $2 \pi$....
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Harmonic oscillator :Two masses are attached to one unfixed spring from both sides (vertically) [closed]

while ($t<0$) the system is still ($\Sigma$ F=0). Mass $m_2$ is held while $t<0$. Mass $m_1$ is located $h_0$ meters above the ground and the spring is currently stretched $L$ meters. The spring'...
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What is the time period of an oscillator with varying spring constant?

It is well known that the time period of a harmonic oscillator when mass $m$ and spring constant $k$ are constant is $T=2\pi\sqrt{m/k}$. However, I would be interested to know what the time period ...
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Confusion about the resonance

I get confused with the concept of resonance. Many materials suggest that in order to achieve resonance, the system must undergo simple harmonic force ($F=F_0\sin(\omega t)$), and at the natural ...
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Eigenstates of a harmonic oscillator

Using ladder operators, I can find eigenstates $\psi_n$ with eigenenergies $$E_n=\hbar\omega\left(n+\frac{1}{2}\right). $$ In my textbook, ladder operators work like $$ a\psi_n = c_n \psi_{n-1}$$ $$ a^...
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Period for small oscillations is like simple harmonic motion

In Arnold's book on mechanics there is the following problem: Consider the period of oscillations near a minimum $E_0$ of the potential energy function $U$. Then he says to compute the limit of ...
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Hooke's Law and Simple Harmonic Motion

Can anyone explain how the following formula is derived and what it means? $$x'' = -n^2x $$ I was reading through my high school physics textbook and I stumbled upon a section on Hooke's Law. It says ...
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Do I have some freedom when I define the quantum SHO ladder operators? [closed]

I tried to solve the quantum harmonic oscillator via the operator method. After doing it and looking up the solution I noticed that for some reason the ladder operators got an additional factor of (i) ...
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Is it true that spring has more force acting on it at its positive maximum amplitude than than at the negative one?

Am I missing something? It seems obvious to me that at $+A$ and $-A$, the spring has restorative forces equal in magnitude but opposite in direction. But since gravity is always pulling it down, ...
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Is harmonic oscillator continuous variable system?

In the literature I have seen that the notions "our system is continuous variable system", "Hilbert space of our system is infinite" were used as if they were equivalent. For example for harmonic ...
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Is the electron-hole pair a 1D quantum oscillator or 3D oscillator

I'm trying to use fluctuation dissipation theorem to describe spontaneous photon emission process by electron-hole recombination in semiconductor material. I notice that all the references using such ...
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Is there an analog to the Runge-Lenz vector for a harmonic potential?

The Runge-Lenz vector is an "extra" conserved quantity for Keplerian $\frac{1}{r}$ potentials, which is in addition to the usual energy and angular momentum conservation present in all central force ...