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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Symbol for dashpot/damper (in a harmonic oscillator)

In diagrams that contain the dashpot symbol, sometimes the mass is attached to the "interior" end of the dashpot, other times the mass is attached to the "base" end. For example, consider the ...
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Time period of torsion oscillation

For the oscillation of a torsion pendulum (a mechanical motion), the time period is given by $T=2\pi\sqrt{\frac{I}{C}}$ which is a result of the angular acceleration ...
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Exact energies of spherical harmonic oscillator in Dirac equation

The potential is given by: $$ V(r) = {1\over 2} \omega^2 r^2 $$ and we are solving the radial Dirac equation (in atomic units): $$ c{d P(r)\over d r} + c {\kappa\over r} P(r) + Q(r) (V(r)-2mc^2) = E ...
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Does the Fundamental Frequency in a Vibrating String NOT Necessarily Have the Strongest Amplitude?

I am doing some experiments on musical strings (guitar, piano, etc.). After performing a Fourier Transform on the sound recorded from those string vibrations, I find that the fundamental frequency is ...
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Why are the solution coefficients for a harmonic oscillator proportional to minors of the determinant?

I'm studying the oscillations of systems with more than one degree of freedom from Landau & Lifshitz's Mechanics Third Edition (for those who have the book, my question corresponds roughly to ...
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Simple step in time evolution of position operator in simple harmonic motion

When considering the 'Heisenberg' picture of the harmonic oscillator, I've come across the step: $$\begin{align} \left\langle n\left|(\hat{q_H}\hat{H}-\hat{H}\hat{q_H})\right|k\right\rangle &= ...
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What's wrong with this equation for harmonic oscillation?

The question: A particle moving along the x axis in simple harmonic motion starts from its equilibrium position, the origin, at t = 0 and moves to the right. The amplitude of its motion is ...
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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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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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Conversion of motion equation from Cartesian to Polar coordinates: Is covariant differentiation necessary?

I have earlier posted the same question here on math stackexchange but without any answer. As the question concerns tensors, I guess that I have come to the right ...
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Does a cycle (in Simple Harmonic Motion) have to equal 2π?

So, I search for the definition of cycle and I get this in Wikipedia: A turn is a unit of angle measurement equal to 360° or 2π radians (or ...). A turn is also referred to as a revolution or ...
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Why are overtones forbidden within the harmonic approximation?

In vibrational spectroscopy only transitions between neighboring vibrational states ($\Delta \nu = \pm 1$, $\nu$ being the vibrational quantum number) are allowed within the harmonic approximation. ...
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When are Maximum Velocity and Acceleration acheived in Simple Harmonic Motion?

Im trying to get my head around SMH out of curiosity because it seems simple yet I'm not getting the concept behind some ideas. For a SMH equation : $$ x=a \sin(\omega t+\phi) $$ Under what ...
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Finding Phase angle of Simple Harmonic Motion?

A sinusoidal oscillator has : $$x=x_{max} \cos(\omega t - \varphi )$$ Period is 2, initial displacement is 100mm initial velocity is 200mm/s What is the phase angle assuming $-\pi < \varphi < ...
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Vibrational motion of linear diatomic molecule

This question concerns the following exercise from an old exam: The vibrational motion of a linear diatomic molecule can be approximated as simple harmonic motion. A CO molecule has a bond ...
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Solutions of damped oscillator differential equation

I am reading about damped harmonic motion in my Physics book (Gerthsen Physik) and there are two things that irritate me: Stokes friction It says that Stokes friction would be $$F = -m \gamma ...
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How to prove that a motion is Simple Harmonic Motion (SHM)?

I would like to know how one could show and prove that a given motion is simple harmonic motion. Once given an answer, I'll apply that technique to an example I am trying to figure out. Thank you ...
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Simple Harmonic Motion. Why am I wrong? Why is my equation wrong more importantly?

Problem/Solution ! I am deeply confused. B) We know that $x = 2\sin(3\pi t)$. $x' = 6\pi\cos(3\pi t)$ So max speed is $6\pi$ $6\pi = 6\pi \cos(3\pi t)$ $\cos(3\pi t) = 1$ $3\pi t = ...
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Why is the angle of a pendulum as a function of time a sine wave?

OK so I'm trying to understand why the angle of a pendulum as a function of time is a sine wave. I can't really find an explanation online and when I do find something partial there are certain ...
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Finding coefficient of proportionality

Recently in my AP Physics class I did a lab in which I measured k for a spring by setting up an oscillating system with it, and timing the period, repeating for different masses. Since ...
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How can I show that an arbitrary wavefunction in a 1D SHO is periodic in time?

I want to show that an arbitrary wavefunction $f$ in a one dimensional harmonic potential reproduces itself after a period T up to a phase factor: $f(x,t+T)=Af(x,t)$, $|A|=1$ I am not sure if this ...
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What are some interesting coupled harmonic oscillators problems?

That I could create as a classical mechanics class project? Other than the classical examples that we see in textbooks.
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Expected number of quanta in harmonic oscillator states

I'm working my way through A Squeezed State Primer, filling in details along the way. Let $a$ and $a^\dagger$ be the usual annihilation and creation operators with $[a,a^\dagger]=1$ and ...
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How can I model a polyatomic molecule as a system of coupled oscillators?

(Classical Mechanics) Let's say I have a polyatomic molecule, what is the best way for finding the equations of oscillations if they are bounded by a torsion spring?
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Inverted Harmonic oscillator

what are the energies of the inverted Harmonic oscillator? $$ H=p^{2}-\omega^{2}x^{2} $$ since the eigenfunctions of this operator do not belong to any $ L^{2}(R)$ space I believe that the spectrum ...
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Amplitude of a Forced Harmonic Oscillator

For an assignment in one of my maths units at uni, I've been asked to derive and solve the differential equation of motion for a forced harmonic oscillator, with the forcing function having the form ...
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3D Quantum harmonic oscillator

For an isotropic 3D QHO in a potential $V(x,y,z)={1\over 2}m\omega^2(x^2+y^2+z^2)$. I can see by independence of the potential in the $x,y,z$ coordinates that the solution to the Schrodinger equation ...
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Help understanding this forced undamped oscillator

I have a forced oscillating system, with driving force as $f_0\cos\omega_0 t \cos \delta t$ giving the equation of motion: $$\ddot{x}(t) +\Gamma \dot{x}(t) +\omega_0^2x(t) = f_0\cos\omega_0 t \cos ...
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Spring oscillations and waves

Consider a block of mass $m$ attached to a spring. Let it oscillate at a frequency $f$. Now each part of the spring is in SHM. so this means a wave is propagating through this spring.bCan this wave be ...
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How do I solve for the phase constant given the amplitude and the angular frequency?

A piston (with mass M) in a car engine is in vertical simple harmonic motion with amplitude A. The engine is running at a period T. Suppose a small piece of metal with mass m were to break ...
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Using Fourier Transforms to Solve Systems with springs of high frequency

I'm trying to numerically solve the differential equations of motion in a system with multiple springs of very high frequency. Because the solution is often a combination of rapidly-oscillating sine ...
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Energy Levels of 3D Isotropic Harmonic Oscillator (Nuclear Shell Model)

One simple way of detailing the very basic structure of the nuclear shell model involves placing the nucleons in a 3D isotropic oscillator. It's easy to show that the energy eigenvalues are $E = ...
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How to calculate viscous damping coefficient?

The damping of a spring is calculated with: $$[\zeta] = \frac{[c]}{\sqrt{[m][k]}}$$ Where c is the 'viscous damping coefficient' of the spring, according to Wikipedia. m is the mass, k is the spring ...
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Degeneracy of states in mixed infinite square well, harmonic oscillator

I'm trying to determine the degeneracy of states given by $g(\epsilon)=g_{0} \epsilon$ for a system that is trapped in a quite specific potential. In two dimensions, the particle has a potential as ...
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How to determine viscous dampening coefficient of spring?

I'm trying to determine the viscous dampening coefficient of a spring $c$. Read about it on Wikipedia here. The two equations which I have are: $f=-cv$ and $ma+cv = -kx$ I know the spring constant ...
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Damping and stiffness constants of water

I'm working on a simulation of water drops falling into a pool. I'm specifically interested in the waves generated by the impact of the drops. In order to calculate the vertical motion of the waves, I ...
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Investigating damped Harmonic Motion in a Spring?

I'm going to conduct an investigation into the dampening of a spring. Essentially, what specific factors could be investigated? Currently I'm planning to investigate the effect of changing the mass ...
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What affects the damping of a spring?

What variables affect the damping of a spring executing simple harmonic motion? What are the independent variables, and what variables would need to be controlled in an experiment? I'm attempting to ...
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Plotting a SHO in matlab [closed]

I have no prior experience of using matlab. My teacher want me to solve this question. I have been trying for a couple of hours now with no luck, please help! The mass of 100 g hanging in a spring ...
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What's a good reference for this classical picture Feynman's talking about?

I have a mathematics background but am trying to educate myself a little about physics. At the beginning of Feynman's QED book (not the popular one) is the following: Suppose all of the atoms in ...
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Tricky spring on a surface question

I have this relative simple-looking question that I haven't been able to solve for hours now, it's one of those questions that just drive you nuts if you don't know how to do it. This is the scenario: ...
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How to determine phase angle for a sinusoidal motion?

If I have an over-damped mechanical system that is excited with a sinusoidal motion. That sinusoidal motion starts with a determined frequency then increases frequency over time. Of course, it is ...
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Explanation: Simple Harmonic Motion

I am Math Grad student with a little bit of interest in physics. Recently i looked into the wikipedia page for Simple Harmonic Motion. Guess, I am too bad at physics to understand it. Considering me ...