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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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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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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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 - f^{*}(t)a^{\...
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31 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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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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86 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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126 views

What is the effect of liquid density on the pitch of a singing wine glass?

In the singing wine glass experiment what's the effect on the frequency produced if the effect of liquids with different densities was tested? Everything else would be kept constant (same glass, ...
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54 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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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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67 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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75 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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40 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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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 $v_{i}$...
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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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36 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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20 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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165 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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91 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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20 views

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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55 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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49 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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97 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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54 views

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 $L=T-V=\frac{m}{...
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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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60 views

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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83 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 ...
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26 views

Angular momentum for elliptic path in 2D isotropic oscillator

Assume a 2D isotropic oscillator, i.e $$U = \frac{1}{2}m\omega^2(x^2+y^2),$$ and assume for simplicity that the oscillator performs elliptical motion, with major axis $A$ and semi-major axis $B$. My ...
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100 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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68 views

Are there any conditions under which the Christoffel symbols can be treated as a damping term in a harmonic oscillator?

(Mathjax did not seem to be working as I composed this question. Hopefully it will kick into action once I post.) Note I am a novice at tensor notation. I am working with the following Lagrangian (...
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Harmonic oscillator: if $E=\frac{1}{2} q \dot{\theta}^2+\frac{1}{2} s \theta^2$ then $\omega=\sqrt{\frac{s}{q}}$?

Consider an harmonic oscillator. Suppose that I manage to write the mechanical energy as a function of a quantity, like the angle $\theta$ in this way $$E=\frac{1}{2} q \dot{\theta}^2+\frac{1}{2} s \...
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30 views

Resonant frequency(s) of system of resonant objects?

I am trying to gain a better understanding of resonance when we are dealing with a coupled system of resonating objects. For example, say we have a single gas bubble in liquid and suppose it ...
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Simple harmonic motion in a horizontally accelerating lift [duplicate]

How would the time period of a pendulum in a lift be if the lift was accelerating horizontally to the right ? My teacher did it by putting a pseudo force "ma" to the left, then getting the resultant ...
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68 views

Period on the phase plane (small oscillations)

I have this formula to calculate the period of a motion in the phase space (plan, in this case) along a phase curve. \begin{equation} T(E)=\int_{x_1}^{x_2}\frac{dx}{\sqrt{2(E-U(x))}} \end{equation} ...
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Why doesn't amplitude affect frequency for an object in simple harmonic motion even though we have an equation relating the two?

I understand conceptually why amplitude doesn't affect frequency (especially when relating to sound - singing louder shouldn't change the frequency of the note I sing). However, the equation for the ...
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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: $d^2x/...
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Why do trees sway?

Resonance can also occur in three dimensions (such as wind induced swaying) I tried to make a free body diagram (I know it is terribly wrong) to find the forces that causes the tree to undergo ...
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Confusion on Time and Ensemble Averages of Classical Harmonic Oscillator

Assume we have a classical harmonic oscillator $$ \ddot{x} = -k^2x.$$ Then the general solutions are of the form $x(t) = x_0cos(kt) + \frac{v_0}{k}sin(kt)$ where $x_0$ and $v_0$ are initial conditions....
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45 views

SHM with acceleration at mean position

Suppose we have an equation of motion as $$\frac{d^2x}{dt^2} = -kx + c,$$ then can it be called a SHM? Since acceleration is still proportional to displacement. But then, how will we define the mean ...
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Does everything in this world vibrate? Why?

I was introduced with something called natural frequency of a body. It was taught us in the chapter Simple Harmonic Motion. Our teacher said that everything in this world has its natural frequency of ...
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38 views

Is there no rotational mechanics for non rigid body? How do we deal with such situations in real life?

I am in 12th grade right now. We have a chapter on Rotational dynamics in which it is clearly stated that it is for rigid bodies. I understand that, Moment of Inertia will remain constant only for ...
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A problem about the harmonic oscillator in Quantum mechanics

When I learned quantum mechanics by reading Griffith's book called Introduction to quantum mechanics, I was confused by his description. In Page 53 of the 2ed edition book, after got the recursion ...
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31 views

Can I determine the maximum acceleration with frequency and magnitude?

Consider a mass oscillating up and down on a spring with negligible energy loss. If only the frequency and magnitude of the oscillation is known, how can one determine the maximum acceleration of the ...
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119 views

Sakurai Exercise 2.17 (Harmonic Oscillator, Ladder operators) [closed]

I the field of the harmonic oscillator and ladder operators I am trying to solve exercise 2.17 from Sakurai and want to proof the following relation $$ \langle x^{2n} \rangle = (2n - 1)!! \langle x^...
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Simple harmonic oscillators [closed]

A block whose mass m is $680$ g is fastened to a spring whose constant k is $65$ N/m . The block is pulled a distnce $x=11$ cm from its equilibrium postion at $x=0$ cm on a frictionless surface and ...
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68 views

Damped Pendulum (generalised)

I know the differential equation for the swinging of a simple pendulum: $\displaystyle\frac{\partial^2\theta}{\partial t^2} + \left(\frac{g}{L}\right)\sin\theta = 0$ where: $L$ is the length of ...
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49 views

Simple Harmonic Motion given velocity and acceleration

I am trying to understand how to relate velocity and acceleration of an object to it's amplitude, period, and frequency given only the following: An object of mass m=20kg moves with SHM along the x-...
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105 views

Time period of a pendulum when a constant horizontal force acts

The time period of a pendulum is given by $$T=2\pi\sqrt{\frac{l}{g}}$$ Will the time period change if a constant horizontal force acts on the pendulum? For example, if a force $F$ acts on the Bob ...