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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Does spatial coupling prohibit resonances due to an external source field?
The harmonic oscillator coupled to a sinodial external source
$$\tfrac{\partial^2 x(t)}{\partial t^2}+\omega_0^2 x(t)=F_0\sin(\omega_\text{ext}\ t),$$
has the solution
$$x(t)=x(0)\cos(\omega_0 t)+C ...
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51 views
Pendulum Wave Period
Recently I've seen various videos showing the pendulum wave effect. All of the videos which I have found have a pattern which repeats every $60\mathrm{s}$.
I am trying to work out the relationship ...
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38 views
Metronome synchronisation applied to swings
The movement of several metronomes can be synchronised when a movable floor is utilised which couples the movement of the different metronomes.
Is it possible to apply this sort of synchronisation to ...
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1answer
179 views
Simulating quantum network of harmonic oscillators
Let's say that I have a system of $n$ particles $p_1,\ldots,p_n\in\mathbb{R}^3$ (where $n$ here is on the order of 10,000). Furthermore, suppose we have a graph $G=(V,E)$ describing some network, ...
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69 views
Standing Waves: finding the number of antinodes
A string with a fixed frequency vibrator at one end forms a standing wave with 4 antinodes when under tension T1. When the tension is slowly increased, the standing wave disappears until tension T2 is ...
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74 views
Simple harmonic oscillator system and changes in its total energy
Suppose I have a body of mass $M$ connected to a spring (which is connected to a vertical wall) with a stiffness coefficient of $k$ on some frictionless surface. The body oscillates from point $C$ to ...
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45 views
Effective mass in Spring-with-mass/mass system
Suppose you have a particle of mass $m$ fixed to a spring of mass $m_0$ that, in turn, is fixed to some wall. I'm trying to calculate the effective mass $m'$ that appears in the law of motion of the ...
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1k views
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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Relativistic genarization of Quantum Harmonic Oscillator
I am trying to find out relativistic description of a quantum harmonic oscillator.
For a classical relativistic oscillator mass is a function of co-ordinates(http://arxiv.org/abs/1209.2876).
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Zero point fluctuation of an harmonic oscillator
In a paper, I ran into the following definition of the zero point fluctuation of our favorite toy, the harmonic oscillator:
$$x_{ZPF} = \sqrt{\frac{\hbar}{2m\Omega}} $$
where m is its mass and ...
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310 views
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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71 views
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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502 views
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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36 views
Compound pendulum clarification?
I read in a book the following about compound pendulum and small displacements:
There are two points only for which the time period is minimum.
there are maximum 4 points for which the time ...
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57 views
Quantum harmonic oscillator. Finding operators
Problem:
I'm trying to verify that $p_H(T)$ and $x_H(T)$ satisfy the following equations, (by solving the Heisenberg equation):
$x_H(t)=x_H(0)cos(\omega t)+(1/m\omega)p_H(0)sin(\omega t)$
...
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72 views
How does an oscillating particle in a non-inertial reference frame appear?
The general question is : given an oscillating particle in a non-inertial reference frame:
How would it appear from outside the non-inertial reference frame ?
How would an observer inside that ...
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46 views
Finding an efficient strategy for walking
Let's say you are already walking at a maximally efficient combination of pace and stride (or $\omega$ and $X_0$ I guess) but you need to reach your destination faster. Should you increase/decrease ...
