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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Simplest explanation of pendulum having a constant time period at low angles

What is the simplest explanation for the pendulum having a constant time period at low angles?
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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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Initial value in rescaling differential equation

I've re scaled the simple harmonic oscillator differential equation as below: original equation: $d^2x/dt^2+\omega^2x=0$ re scaling factor: $\omega t\to t'$ re scaled (dimensionless) equation: ...
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Coupled quantum harmonic oscillator

Given the following Hamiltonian for two identical linear oscillators with spring constant $k$ and interaction potential $\alpha x_1x_2$; I was asked to find the expectation value $\langle ...
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1answer
37 views

A problem on Doppler's Effect [on hold]

A source of sound emitting a frequency of 660 Hz is moving counter-clockwise in a circular path of radius 2 m with an angular velocity 15 rad/s. A recorder at a distance from the source is moving ...
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2answers
61 views

Simple harmonic motion angular frequency [on hold]

I'm struggling with this physics question. "A simple harmonic wave of wavelength 16 cm and amplitude 2.5 cm is propagating along a string in the negative x-direction at 35 cm/s." a) Find its angular ...
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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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Transverse simple harmonic wave travelling in a string [on hold]

This question came in my exam. My Attempt: I thought that the tension will not vary in the string because since we know that velocity of wave in a string is given by $$v=(T/m)^{1/2} $$ where $v$ ...
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32 views

Can maximum KE and maximum PE be different in SHM? [closed]

In simple harmonic motion of particle maximum kinetic energy is 40J And maximum potential energy is 60J. Then what is minimum potential energy?
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1answer
67 views

Do you know the principle which says that connecting two sources of similar kind produces a waste and destruction? [closed]

There is a great article, called commutation cells, which states that you cannot transfer kinetic energy from one container to another immediately, bypassing the potential energy storage. Otherwise, ...
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1answer
46 views

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
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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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1answer
24 views

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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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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5answers
142 views

A conceptual doubt regarding Forced Oscillations and Resonance

While studying about the Resonance and Forced Oscillations, I came across a graph in my textbook that is given below:- Now, the author writes As the amount of damping increases, the peak shifts ...
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1answer
44 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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2answers
143 views

Does spatial coupling prohibit resonances due to an external source field?

The harmonic oscillator coupled to a sinodial external source $$\frac{\partial^2 x(t)}{\partial t^2}+\omega_0^2 x(t)=F_0\sin(\omega_\text{ext}\ t),$$ has the solution $$x(t)=x(0)\cos(\omega_0 t)+C ...
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2answers
67 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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Why doesn't mass of bob affect time period?

The gravitation formula says $$F = \frac{G m_1 m_2}{r^2} \, ,$$ so if the mass of a bob increases then the torque on it should also increase because the force increased. So, it should go faster and ...
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1answer
153 views

Cause of SHM of liquid-column in V-tube

Suppose there is a v-shaped tube filled with water. The left limb is at $\theta_1$ & the right limb is at $\theta_2$ with the horizontal base. Initially, the level of water in both the columns are ...
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2answers
38 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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2answers
87 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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1answer
104 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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2answers
629 views

Green function for simple harmonic oscillator

I'm interested in examples on how to use Green function (GF)for simple harmonic oscillator (SHO)? I am from undergrad physics, so I need a fundamental math and quantum mechanical application of GF ...
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2answers
67 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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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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1answer
59 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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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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60 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
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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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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1answer
70 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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1answer
25 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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55 views

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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1answer
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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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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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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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Why do electromagnetic waves oscillate?

I've been considering this question, and found many people asking the same (or something similar) online, but none of the answers seemed to address the core point or at least I wasn't able to make ...
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60 views

Pendulum at an angle

A pendulum has a period of $T$ when swinging from a string. The pendulum is now placed on a frictionless incline at a 30 degree angle. What is the new period of the pendulum?
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1answer
22 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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2answers
93 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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1answer
46 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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Using $\sin()$ or $\cos()$ for computing SHM?

In simple harmonic motion, you can use either the sin or cos form of the equation but my question is which one do you use when and why? I am having a tough time understanding this, so any help would ...
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1answer
130 views

One body harmonic oscillator states expressed in terms of creation operators

I am reading trough chapter one of Moshinsky's "The harmonic Oscillator in Modern Physics". However i am having some trouble with the mathematics in section 8 of chapter 1. I will sketch a summary of ...
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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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1answer
55 views

Complex resonant frequency not resonant without imaginary part. So can I still just take real part as solution?

I am working with a matrix on a harmonic oscillator problem and the lowest (absolute) frequency $\omega_0$ where the matrix becomes singular is the resonant frequency. Now I obtained this frequency ...
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1answer
46 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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860 views

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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1answer
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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.