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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Mass spring system, increase mass [closed]
The question says that after a mass $m=M$ (attached to a horizontal spring) reaches its furthest point, so at its amplitude, the mass is doubled, $m=2M$.
What happens to the period, amplitude and ...
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3answers
483 views
Partition function for quantum harmonic oscillator
Hi guys I'm currently trying to solve a mock exam for an exam in a few days and am a bit confused by the solutions they gave us for this exercise:
Exercise:
A solid is composed of N atoms which ...
14
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1answer
583 views
Why don't tuning forks have three prongs?
I was reading Why tuning forks have two prongs?. The top answer said the reason was to reduce oscillation through the hand holding the other prong.
So if having 2 prongs will reduce oscillation loss, ...
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3answers
838 views
How to derive the period of spring pendulum?
So I wanted to find out how to (simply, if that's possible) derive the formula for a period of spring pendulum: $T=2\pi \sqrt{\frac{m}{k}}$. However, Google doesn't help me here as all I see is the ...
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2answers
309 views
Dynamics of a Vertical Mass-Spring Simple Harmonic Oscillator with Gravity
I am having some trouble obtaining the elastic potential energy and gravitational potential energy of a simple mass spring system.
In this experiment, masses attached to a spring were dropped from a ...
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1answer
316 views
Estimate the damping coefficient of my car
I was wondering how I can estimate the damping coefficient of my car by doing the hand bouncing the car body and watching the motion of the car?
I just need a rough estimate of the damping ...
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1answer
280 views
Writing equation for amplitude of driven harmonic oscillator in Lorentzian form
This harmonic oscillator is driven and damped, with the form:
$$\ddot{x} + \lambda \dot{x} + \omega_0^2 x = A \cos(\omega_d t)$$
Now, I have used the ansatz (guess): $x(t) = B \cos(\omega_d t + ...
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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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180 views
Finding an equation for velocity and acceleration
I'm trying to derive an equation for the velocity and acceleration of an object undergoing simple harmonic motion.
I have the equation for displacement: $x = A\sin (2 \pi ft)$
If I differentiate the ...
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2answers
165 views
Definition of “Quantizing”
Could anyone explain to me what "quantize" means in the following context?
Quantize the 1-D harmonic oscillator for which
$$H~=~{p^2\over 2m}+{1\over 2} m\omega^2 x^2.$$
I understand that the ...
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1answer
81 views
Noise spectrum of two systems and interacting Hamiltonian
I've been discovering recently the concept of noise spectrum, defined as:
$$S_{xx}[\omega] = \int dt<x(t)x(0)>\text{e}^{-i\omega t}$$
Roughly the Fourrier transform of the two-point function.
...
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2answers
125 views
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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2answers
359 views
Non-Degeneracy of Eigenvalues of Number Operator for Simple Harmonic Oscillator [duplicate]
Possible Duplicate:
Proof that the One-Dimensional Simple Harmonic Oscillator is Non-Degenerate?
I'm trying to convince myself that the eigenvalues $n$ of the number operator ...
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2answers
296 views
Showing that the probability density of a linear harmonic oscillator is periodic
The complete question I am trying to answer is the following:
Show that the probability density of a linear harmonic oscillator in an arbitrary superposition state is periodic with period equal to ...
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2answers
186 views
Harmonic oscillator and Lorentz symmetry
There is a analog between harmonic oscillator $x=\frac{1}{\sqrt{2\omega}}(a+a^\dagger)$ and quantum field $\phi=\int dp^3\frac{1}{(2\pi)^3}\frac{1}{\sqrt{2\omega_p}}(a_p e^{ipx}+a^\dagger e^{-ipx})$, ...
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2answers
403 views
Expectation value of time-dependent Hamiltonian
I'm trying to solve a problem in QM with a forced quantum oscillator. In this problem I have a quantum oscillator, which is in the ground state initially. At $t=0$, the force $F(t)=F_0 \sin(\Omega t)$ ...
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1answer
636 views
Evolution operator for time-dependent Hamiltonian
When i studyed QM I'm only working with non time-dependent Hamiltonians. In this case unitary evolution operator has the form $$\hat{U}=e^{-\frac{i}{\hbar}Ht}$$ that follows from this equation
$$
...
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1answer
186 views
Spectrum of quantum fluctuations in a harmonic oscillator
If we have a harmonic oscillator and look at it on small scale the energy is quantized and we can calculate the different eigenstates. In general the energy eigenvalues are given by $$E_n = ...
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2answers
442 views
What is the formula for max kinetic and max potential energy of a spring?
What is the formula for max kinetic and max potential energy of a spring?
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1answer
88 views
Strange Behavior in Spring Computer Model
To learn more about oscillatory motion which I am learning about in my high school physics class, I have created a computer model of a damped spring where the damping force is proportional to ...
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47 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 ...
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2answers
149 views
Understanding the concept of period of motion in simple harmonic motion formula
I have a spring system, whose position equation is $$x(t) = c_1cos(8 \sqrt{2}t) + c_2sin(8 \sqrt{2}t)$$
The textbook says it will have a period of motion of $\frac{2 \pi}{(8 \sqrt{2}t)}$. I ...
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1answer
208 views
Basis transformation between eigenstates of harmonic oscillators with different frequency
Given two harmonic oscillators with frequencies $\Omega$ and $\Omega'$, the eigenstates themselves are exactly known. Let's call them $\Psi_n$ and $\Psi'_n$.
Is there a compact expression for the ...
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1answer
146 views
How do eigenstates of harmonic oscillators with different frequencies compare?
Suppose I have a harmonic oscillator with frequency $\Omega_1$ and another one with frequency $\Omega_2$. Is there a simple relationship between the eigenstates of the two? Especially, how would the ...
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1answer
143 views
Spring-mass physics homework question [closed]
I've been having trouble with my physics homework. The problem is:
You may have measured the properties of a simple spring-mass system in the lab. Suppose you found ks = 0.9 N/m and m = 0.01 kg, ...
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2answers
263 views
Linear motion with variable acceleration
Consider the following problem
I pull a mass m resting at x = 0 on a frictionless table connected to a spring with some k by an amount A and let it go. What will be its speed at x=0?
I know how to ...
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1answer
183 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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499 views
Finding the period and frequency for simple harmonic motion [closed]
A 1 lb weight is suspended from a spring. Let y give the deflection (in inches) of the weight from its static deflection position, where “up” is the positive direction for y. If the static ...
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1answer
63 views
Does every wavenumber of IR result in a different kind of vibration?
Does every wavenumber of IR result in a different kind of vibration?
If that is true, what if a molecule absorb 2 different wavenumbers (which cause different rocking and symmetrical stretching for ...
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2answers
127 views
Frequency of a tuning fork in a vacuum
Consider this equation of a damped harmonic oscillator such that:
$$
\ddot{x}+2\gamma\dot{x}+\omega^2_0=0
$$
with: $\gamma=\frac{b}{2m}$ and $\omega_0=\sqrt{\frac{k}{m}}$
Finally, we know that the ...
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2answers
461 views
Using eigenvalues to determine the stability/behaviour of the system
first time I've been on physics.se but have used the math and cs before...
Anyway, here's my question:
If we have a damped pendulum described by the equation $$y'' + ay' + b = 0 , a>0$$ Using the ...
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2answers
241 views
How to think of the harmonic oscillator equation in terms of “acceleration = gradient”
This is related to another question I just asked where I learned that the equation of motion of a harmonic oscillator is expressed as:
$$\ddot{x}+kx=0$$
What little physics I grasp centers on ...
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1answer
188 views
Question on Sakurai's treatment of the Harmonic Oscillator:
In Section 2.3 of the second edition of Modern Quantum Mechanics (which discusses the harmonic oscillator), Sakurai derives the relation $$Na\left|n\right> = (n-1)a\left|n\right>,$$ and states ...
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2answers
112 views
Force to use in harmonic oscillation through the inside of a planet
I am to find an equation for the time it takes when one falls through a planet to the other side and returns to the starting point. I have seven different sets of values - mass of object falling, mass ...
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Capsule traveling through a planet, find time for return [duplicate]
Possible Duplicate:
If it was possible to dig a hole that went from one side of the earth to the other
A corporation is building attractions in outer space, in which they drill tunnels ...
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1answer
160 views
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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3answers
531 views
Time period of torsion oscillation
The time period for a wave of frequency $\nu$ is given by $T = \frac{1}{\nu}$ or in other words, $T=\frac{2\pi}{\omega}$ where $\omega$ is the angular velocity...
For the oscillation of a torsion ...
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1answer
495 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):
$$
c{d P(r)\over d r} + c {\kappa\over r} P(r) + Q(r) (V(r)-2mc^2) = E ...
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3answers
310 views
Does the Fundamental Frequency in a Vibrating String NOT Necessarily Have the Strongest Amplitude?
I am doing some experiments on musical strings (guitar, piano, etc.). After performing a Fourier Transform on the sound recorded from those string vibrations, I find that the fundamental frequency is ...
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2answers
191 views
Why are the solution coefficients for a harmonic oscillator proportional to minors of the determinant?
I'm studying the oscillations of systems with more than one degree of freedom from Landau & Lifshitz's Mechanics Third Edition (for those who have the book, my question corresponds roughly to ...
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2answers
127 views
Simple step in time evolution of position operator in simple harmonic motion
When considering the 'Heisenberg' picture of the harmonic oscillator, I've come across the step:
$$\begin{align}
\left\langle n\left|(\hat{q_H}\hat{H}-\hat{H}\hat{q_H})\right|k\right\rangle &= ...
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1answer
631 views
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 ...
8
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2answers
958 views
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 $\{\vert n \rangle\}_{n = ...
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3answers
294 views
Is the quantization of the harmonic oscillator unique?
To put it a little better:
Is there more than one quantum system, which ends up in the classical harmonic oscillator in the classial limit?
I'm specifically, but not only, interested in an ...
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1answer
1k views
Conversion of motion equation from Cartesian to Polar coordinates: Is covariant differentiation necessary?
I have earlier posted the same question here on math stackexchange but without any answer. As the question concerns tensors, I guess that I have come to the right ...
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2answers
324 views
Does a cycle (in Simple Harmonic Motion) have to equal 2π?
So, I search for the definition of cycle and I get this in Wikipedia:
A turn is a unit of angle measurement equal to 360° or 2π radians (or ...). A turn is also referred to as a revolution or ...
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2answers
191 views
Why are overtones forbidden within the harmonic approximation?
In vibrational spectroscopy only transitions between neighboring vibrational states ($\Delta \nu = \pm 1$, $\nu$ being the vibrational quantum number) are allowed within the harmonic approximation. ...
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2answers
3k views
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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1answer
1k views
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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1answer
311 views
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 ...
