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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When a particle oscillates with simple harmonic motion, the period of the oscillation is [on hold]

When a particle oscillates with simple harmonic motion, the period of the oscillation is... a) ...directly proportional to the displacement from the origin b) ...directly proportional to the ...
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40 views

Why does a bungee jumper continue to move downwards beyond the equilibrium position of the jumper and cord?

When a bungee jumper jumps, ignoring the mass of the bungee cord, the jumper initially falls in freefall before an inelastic collision occurs between the jumper and cord, and the cord extends as the ...
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45 views

Resonant Frequency of 2 mass spring system

So the question goes if I has a spring with spring constant $k$ and two masses attached to this spring (one on either side) what is the resonant frequency of the system in terms of $m$ and $k$? ...
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Why do standing waves only occur in some specific conditions?

In the string which has both end fixed then the end point have to be $n (\lambda/2)$ from the beginning point in order to have standing waves. I know it has to start with a node and end with a node, ...
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Period of a simple pendulum [on hold]

A simple pendulum hung in an elevator had a period of T when the elevator is at rest . What is the period of this pendulum when the elevator moves upward with an acceleration of $a$? I need to get the ...
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Simple harmonic motion equation with defined initial velocity and final velocity [closed]

I have been working with simple harmonic motion (SHM). I can use SHM to create CAM tables that map Master positions with Slave positions. I specify an initial Master Position that corresponds to an ...
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198 views

Why do the ladder operators in harmonic oscillators work?

The Hamiltonian can be diagonalized by transforming $x$ and $p$ to $a$ and $a^\dagger$. I understand how one proceeds from there to find the spectrum of $a^\dagger a$, the ground state $|0\rangle$ and ...
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1answer
57 views

Equation of Motion for spring-cylinder-mass system [closed]

Hello, I hope someone can help me with this question, to find the equation of motion of the disc for small angular rotations. The mechanism comprises of a uniform circular disc of mass $m$, spring ...
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39 views

Damped Simple Harmonic Motion Proof? [closed]

I was reading about damped simple harmonic motion but then I saw this equation: $$-bv - kx = ma$$ $b$ is the damping constant. Then it said by substituting $dx/dt$ for $v$ and $d^2x/dt^2$ for $a$ we ...
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559 views

Spring pendulum - why is it possible to use this equation?

It is known that, when we describe the spring pendulum, we are bound to use the formula $T = 2\pi \sqrt{m/k}$, however, we can go further and set $\omega = \frac{2\pi}{T}$ I ponder why is this ...
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27 views

Mechanical energy in an harmonic wave and in normal modes

I think I miss something about energy of a mechanical wave. In absence of dissipation the mechanical energy transported by an harmonic wave is constant. $$E=\frac{1}{2} A^2 \omega^2 m$$ But, while ...
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Annihilation operator in harmonic oscillator

In Wikipedia's QHO page there is a moment when the following is stated: I don't know why "the ground state in the position representation is determined by $a|0\rangle=0$". I would say that the ...
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Physical motivation for one dimensional SHM superposition

Are there any real life, simple and mechanical system which motivate the study of Simple Harmonic Motion (SHM) superposition in one dimension? I am preparing a lecture about it but I have not seen any ...
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23 views

Simple harmonic waves

When a simple harmonic progressive wave is travelling through medium,then each succeeding particle lags in phase before the preceding particle.Can anyone expain how does it lag? Thanks…
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124 views

Transverse Wave [closed]

Tranverse Wave is travelling in a string.
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67 views

SHO in QM and Klein Gordon field in 1+0D QFT

The SHO in QM with mass $m=1$ has action $$ S[x] = \int dt \frac{1}{2} \dot x^2 + \frac{1}{2}\omega^2 x^2 $$ by integration by parts we see this is the same as 1 dim Klein Gordon QFT action with ...
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Velocity in harmonic motion - Why are these angles congruent?

I learned about harmonic motion and I found the derivation of the formulas: And so, the velocity in harmonic motion is the projection of the velocity in angular motion. The only thing that is not ...
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1answer
47 views

Amplitude of damped driven harmonic oscillator [closed]

I have a question that I can reason physically but mathematically I am not sure if my approach is correct. The amplitude of the oscillator is: $$A(\omega) = \frac{QF_{0}}{m}(\frac{1}{\omega_{0} ...
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69 views

What information am I losing out when I assume that the displacement in S.H.M. is small?

While making calculations for simple harmonic motion, we take the force as $F=F(x)$. Then we use Taylor's expansion and calculate as follows: $$\begin{align} F(x) &=F(0+x) \\ & = ...
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Deriving eigen values of $\hat{N}$

So let's say we have an operator $\hat{a}$ (ladder operator), where $\left[\hat{a},\hat{a}^\dagger\right] = 1$, and $\hat{a}^2 |\phi\rangle = 0$. How do I show that the eigenvalues of ...
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2answers
39 views

Degrees of degeneracy of energy values

Let us consider the harmonic oscilator in three dimensions whose hamiltonian is: $$H = \dfrac{1}{2m} \mathbf{P}^2+\dfrac{m\omega^2}{2 }\mathbf{R}^2.$$ The nicest way to solve the eigenvalue equation ...
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88 views

Which coordinate is to be considered for the energy of simple pendulum?

For an simple harmonic oscillator energy can be represented as in picture. Consider in particular picture (b) with the energy as a function of the coordinate $x$. Consider now a simple pendulum. The ...
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107 views

Three dimensional isotropic harmonic oscilator Hamiltonian

Let us consider the Hamiltonian for the isotropic three dimensional harmonic oscilator: $$H = \dfrac{\mathbf{P}^2}{2m}+\dfrac{m\omega^2\mathbf{R}^2}{2},$$ where $\mathbf{P}$ and $\mathbf{R}$ are the ...
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68 views

Free particle and harmonic oscillator coupled

I'm currently playing with a toy model given by the Lagrangian $$L=\frac{m\dot{x}^2}{2}+\frac{m\dot{y}^2}{2}+\frac{1}{2}m\omega^2x^2+x y,$$ which is basically a free particle (described by $y(t)$) and ...
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Variation of the effective spring constant of a trampoline-like arrangement of springs with diameter

I'm currently investigating the simple harmonic motion of the following system of springs: The second diagram represents the center mass executing simple harmonic motion up and down about the ...
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64 views

Instantaneous energy eigenstates for forced harmonic oscillator

I'm interested in applying the adiabatic theorem to the forced harmonic oscillator with time dependent hamiltonian of the form: $$H(t) = \hbar \omega(a^{\dagger}a + \frac{1}{2}) - f(t)a - ...
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Phase difference in SHM between spatial coordinate and velocity

In simple harmonic motion the spatial coordinate $x(t)$ and the velocity $v(t)$ have a phase difference of $\frac{\pi}{2}$ and I'm totally ok with that. But I also saw that the difference in the phase ...
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21 views

Quanta exchange between 2 harmonic oscillators during an Otto cycle

The focus of my current studies lies on the "Quantum Otto cycle" (e.g. presented on the first pages of this paper). The "machine" as well as the "baths" are represented by harmonic oscillators. Both ...
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62 views

Pendulum on a train

I've seen multiple questions about a pendulum on a train and most say to use $T = 2 \pi (L/F)^{1/2}$ and I have done this to compare the pendulum's periods before being on a train and then once its on ...
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1answer
51 views

Possible duality between Harmonic oscillator and free particle?

There is some connection between classical non-interacting harmonic oscillator (OH) and the free particle in higher dimensions? I was studying statistical mechanics and I came across the idea that ...
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24 views

Ideas for a Torsional Spring

For a physics laboratory I have been tasked with building an effective torsional pendulum that must be able to time up to five minutes. I have been researching the best materials to use for the ...
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62 views

Ladder Operators

I want to show that the following formula for the ground state $\psi_0$ of the harmonic oscillator is valid:$$<\psi_0,\hat x^{2n}\psi_0>=\frac{(2n)!}{2^{2n}n!}(\frac{h}{m \omega})^n$$Ok I want ...
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71 views

Driven harmonic oscillator [closed]

Given the Hamiltonian of a loaded particle $$\hat H = \frac{\hat p^2}{2m}+eE(t) \hat x + \frac{1}{2}m\omega^2 \hat x^2$$ show that The time dependent expected values $\langle \hat p\rangle$ and ...
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33 views

Real-World Example for the Horizontal Spring-Block Oscillator

I am wondering whether there exists a spring that behaves like those shown in a multitude of physics textbooks, where a mass stretched/compressed to a certain point oscillates back and forth in some ...
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1answer
31 views

Frequency of oscillator

We are given an undamped simple harmonic oscillator, and two positions $x_{1}, x_{2}$ with the corresponding velocities $v_{1}, v_{2}$. We want to find its frequency in terms of the $x_{i}$ and ...
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Why can some oscillations be modeled by Simple Harmonic Motion, while others cannot?

For some oscillators an increase in the driving amplitude changes the period (frequency) of the oscillation, but the simple harmonic oscillator does not predict this type of behavior. Why?
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How to find positions in the equilibrium state of mass-spring system?

I've simulated 3D mass-spring system (mesh/network). First the system was in equilibrium state of it own (called state {A}). If I moved some of the masses in the system to the new positions, the ...
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1answer
27 views

How does the effective force constant of a trampoline-like system of springs change with the diameter of the trampoline

So, for a school project, I decided to investigate the SHM of a trampoline like system of springs. Basically, I took an ring, affixed eight springs (at equal angle from each other) to a central ...
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18 views

Potential energy of Spring and its oscillation frequency [closed]

Can the energy obtained from the relation between the frequency, spring constant and reduced mass of a spring be equated to the potential energy of the spring?
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112 views

Symmetry and degeneracy in quantum mechanics

If an operator commutes with the Hamiltonian of a problem, does it always must admit degeneracy? For example, parity operator commutes with the Hamiltonian in case of a free particle and we have two ...
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62 views

Mass Spring System on Moon

If we take a vertically hanging mass on a spring and move it to the moon where gravity is roughly 1/6 that of earth, but force it to oscillate at the same amplitude as it did on earth, what doesn't ...
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Does logarithmic decrement take into account an increasing period?

I am trying to determine the 'viscous damping coefficient', c, for a mass/Spring system oscillating vertically in water. I was going to use the logarithmic decrement method to determine the damping ...
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50 views

AC Electricity as a Simple Harmonic Oscillator

Can the net motion of electrons in an AC circuit be considered an example of simple harmonic oscillation. Furthermore, how can the general formulae of SHM be adapted to suit a scenario of an AC ...
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1answer
45 views

Are ALL vibrations an exchange of kinetic and potential energy?

I'm taking a course on mechanical vibrational analysis and this is what I was told by my professor, but I'm curious if there are any counter-examples.
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96 views

Oscillation of non-uniform plank on parallel springs

A plank of length $l$ and mass $m$ is placed on two parallel springs, each with spring constant $k$ and equidistant from the plank's horizontal center of gravity. When the plank is displaced from it's ...
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Relativistic oscillator vs. non relativistic oscillator

Consider a particle of mass $m$ that is constrained to move under the potential $U=k|x|$. In the case where the particle's motion is non-relativistic, the Lagrangian for the motion is ...
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Simple harmonic motion..direction of acceleration

To solve questions about simple harmonic motion, my book says $\ddot{x}$ (i.e. acceleration) is in the direction of increasing $x$, i.e. away from equilibrium. I don't understand why is this so, since ...
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Position Measurement of Quantum Harmonic Oscillator, to a Position Eigenstate

I read that if one takes a quantum harmonic oscillator system, not externally driven, and performs a position measurement (measurement in position basis) that reduces the oscillator to an eigenstate ...
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57 views

Period of simple pendulum accelerated horizontally

I'm confused about simple pendulum problems where the pendulum is accelerated horizontally of anyway not vertically with acceleration $\vec{A}$. $m\vec{g} + \vec{T}-m \vec{A} =m \vec{a}$ So ...
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How can amplitudes be treated as vectors in Simple Harmonic motion?

The amplitudes of 2 SHM are scalors. When we combine the two SHM eq.(lying along the same line), the resultant expression becomes of amplitudes treated as vectors and the phase angle between them as ...