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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Why is the damping force acting on an oscillating system opposite in direction to velocity and not acceleration?

So far I know that the damping force is a frictional force that opposes motion and so it acts in the opposite direction to velocity . Bit why can't the same be said for acceleration doesn't the ...
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2answers
32 views

Springs acting on a car [on hold]

I am trying to solve a problem but I can't figure out why the answer comes out to be what it is: A man of 80kg enters a car and compresses the 4 springs of the car, causing a change of 1,2cm from ...
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1answer
28 views

Oscillation of a simple pendulum [closed]

What is maximum possible time period of oscillation of a simple pendulum on earth? Please elaborate your answers.
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14 views

Modelling a flow due to an oscillating hemisphere?

Say I have a long cylinder filled with air, closed at one end and open at the other. Now say I place a compressible hemisphere at the closed end and make it oscillate (compression and expansion of the ...
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2answers
88 views

How to form the matrix representation of $|O|^3$

I'm interested in getting the matrix representation of the absolute value of an operator. I know the matrix representation of the operator $O$. Now how do I take its absolute value?
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2answers
92 views

The “harmonic paradigm” in physics

Disclaimer: I know this is a vague question, so if this is not the appropriate thread, please direct me to the correct one. On page 5 of Anthony Zee's Quantum Field Theory in a Nutshell he speaks of ...
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1answer
42 views

Expectation energy for a quantum harmonic oscillator

At 59:14 in this video, the expectation value of the energy of a harmonic oscillator is $$ \langle E \rangle = \int ||\tilde{\Psi}(p)||^2 \frac{p^2}{2m}\ \mathrm dp + \int ||\Psi(x)||^2\frac{m\omega^2}...
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0answers
27 views

Galileo's pendulum and any references

In some texts about the simple pendulum we use to see references about some "experiments" Galileo Galilei did realize and whereby he found some important results, including that the period of the ...
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1answer
67 views

Understanding Quantum Harmonic Oscillator derivation

I'm using this pdf as a reference. Basically, I want to solve equation 0.3, which can be simplified to equation 0.5. The solution is in the form $$ \Psi(u)=h(u)e^{\frac{-u^2}{2}}$$ where $h(u)$ can ...
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0answers
37 views

How can $\hat p = - i \hbar \partial_q$ be derived starting from the definitions of $\hat q$ and $\hat p$ in terms of creation/destruction operators? [duplicate]

Consider the position and momentum operators $\hat q$ and $\hat p$, defined respectively in terms of creation and destruction operators in the usual way: $$ \hat q = c (\hat a + \hat a^\dagger), \...
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0answers
18 views

Relation between Qualiy factor and FWHM

I know how to show that the Quality factor $Q=\omega/\nu$ of a damped harmonic oscillator (for example like in this link: http://farside.ph.utexas.edu/teaching/315/Waves/node11.html). What I don't ...
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4answers
44 views

Pendulum and simple harmonic motion

I have a physical pendulum that, for small oscillations, can be modeled with the simple harmonic motion approach. In determining the motion equation, I need to figure out the amplitude: I know that ...
0
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1answer
71 views

Common basis for angular momentum and Hamiltonian, harmonic oscillator

Suppose a two dimensional isotropic harmonic oscillator. We define the angular momentum operator as $L = XP_y - YP_x$, where $X,Y$ are the position operators and $P_x,P_y$ are the momentum operators. ...
2
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1answer
75 views

Relationship between zero modes and symmetry in a simple system of coupled springs

This Wikipedia page states that "zero modes appear whenever a physical system possesses a certain symmetry," and gives the example of a ring of beads connected by springs having a zero mode associated ...
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2answers
41 views

Independence of Period and Amplitude in Simple Harmonic Motion

In Simple Harmonic Motion, the period $T$ of an oscillation, is said to be independent of the amplitude $A$ of an oscillation, but why is that so? Attempting to derive from the equations of Simple ...
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7answers
2k views

Why is the simple harmonic motion idealization inaccurate?

While in my physics classes, I've always heard that the simple harmonic motion formulas are inaccurate e.g. In a pendulum, we should use them only when the angles are small; in springs, only when the ...
3
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1answer
41 views

Is this a valid way for deriving the ODE for a lattice vibration of a one dimensional crystal?

Consider the following lattice: I want to derive a differential equation that describes the forces acting on the $n$-th atom in the lattice. Each atom is coupled to its neighbour ($n+1,n-1)$ by a ...
0
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1answer
43 views

normal force on a physical pendulum [duplicate]

I have read and understood that a normal force has got nothing to do with torque on a physical pendulum. But I can't understand in which direction the normal force points to. Can someone help? This ...
0
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1answer
47 views

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

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 ...
0
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1answer
44 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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3answers
63 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 $k$? ...
0
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2answers
39 views

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, ...
3
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2answers
209 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 ...
1
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1answer
63 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 ...
0
votes
2answers
42 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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3answers
570 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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0answers
39 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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2answers
46 views

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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0answers
29 views

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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2answers
25 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…
5
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3answers
132 views

Transverse Wave [closed]

Tranverse Wave is travelling in a string.
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2answers
70 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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0answers
13 views

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
49 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} \...
0
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2answers
70 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) \\ & = F(0)+xF'(0)+...
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1answer
47 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 $\hat{N}=\hat{...
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votes
2answers
40 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 ...
1
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2answers
90 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 ...
1
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1answer
110 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 ...
0
votes
2answers
74 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 ...
0
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0answers
30 views

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 ...
3
votes
1answer
67 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 - f^{*}(t)a^{\...
1
vote
1answer
30 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 ...
0
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0answers
22 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 ...
1
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2answers
84 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
52 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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0answers
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 ...
1
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1answer
65 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 ...
2
votes
1answer
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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1answer
38 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 ...