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9
votes
2answers
447 views

Small oscillations of heavy string

I'm solving problem in classical field theory and I have some difficulties. I'm trying to study small oscilations of heavy string with fixed points. First of all I wrote down this Lagrangian: ...
0
votes
2answers
102 views

Physical interpretation of initial conditions for damped mass-spring system

I have background in pure mathematics so my question is about physical meaning. If we consider equation for damped mass-spring system, it is linear ordinary second order differential equation. So to ...
6
votes
1answer
146 views

Caldeira-Leggett Dissipation: frequency shift due to bath coupling

I am trying to understand the Caldeira-Leggett model. It considers the Lagrangian $$L = \frac{1}{2} \left(\dot{Q}^2 - \left(\Omega^2-\Delta \Omega^2\right)Q^2\right) - Q \sum_{i} f_iq_i + ...
1
vote
1answer
145 views

Oscillation of a Bose Einstein condensate in a harmonical trap

We were asked to try to make a theoretical description of the following phenomenon: Imagine a 2D Bose Einstein condensate in equilibrium in an harmonical trap with frequency $\omega$. Suddenly the ...
0
votes
1answer
29 views

Correlation between equations of elliptical orbits and pendulums

The equation for the period of a pendulum is: $$T=2π\sqrt{\frac{L}{g}}$$ Where 'g' is the acceleration due to the gravitational field and 'L' is the length. The equation for the period in of a body ...
4
votes
0answers
128 views

Relation of the Bloch-Siegert shift to the rotating pot lid

I see in Wikipedia that the Bloch-Siegert shift is analogies to the rotating pot lid, could you explain that analogy? The Bloch-Siegert shift is a phenomenon in quantum physics that becomes ...
3
votes
0answers
2k 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 = ...
2
votes
0answers
97 views

After quantization of electron vibrations, do we need electrons anyway?

The title question is not ment in a general context, but one in which goes to the plasmon theory. In that case, how is are the statistics (boson vs. fermions) of plasmons determined? And is there an ...
1
vote
0answers
21 views

Confusion regarding the trial solution taken in the mathematical treatment of forced oscillations, at steady state

In the text-book that I am currently using, it is given that in case of forced oscillations, the periodic external driving force is a complex-driving force, and is generally of the form $F_0e^{jwt}$. ...
1
vote
0answers
65 views

Energy of RLC circuit

If you are given a general differential equation for an RLC circuit, for example, $$L\left(\frac{d^2 Q}{dt^2}\right) + R\left(\frac{dQ}{dt}\right) + \frac QC = V\cos(\omega t),$$ which is a driven ...
1
vote
0answers
26 views

Methods for quantifying a network of coupled oscillators

I usually am more on the statistics part of things, so pardon my misuse of the terminology. I am simulating a network of non-pulse coupled non-linear oscillators ( I am not sure what the correct term ...
1
vote
0answers
28 views

Is having full information about the resonances of a rigid body equivalent to having full information about its material parameters?

Lets say I have a mechanical system whose mechanical resonances (mode shape and frequency) I can measure with perfect accuracy. Is this theoretically equivalent to knowing the materials parameters, ...
1
vote
0answers
57 views

stopping, moving of mobile phone when vibrating

A mobile phone move aside when it vibrates. How is that happening ? and most importantly is it possible to make any changes to the vibration motor to stop moving when vibrating or any other methods to ...
1
vote
0answers
44 views

“Forgetting” the initial condition in conservative oscillations; What has been “forgotten” exactly?

I am training myself on oscillations. The topic is self-sustained oscillations. The claim is these oscillations are NOT forgetful about their initial condition as opposed to conservative oscillators ...
1
vote
0answers
280 views

Anharmonic oscillator solution function

I am solving a CLASSICAL an-harmonic oscillator problem with Hamiltonian given by $H= (1/2)\dot{x}^2+(1/2)x^2-(1/2)x^4$ with all the constants (k's) and mass being taken as 1 (one). I find that $x= ...
1
vote
0answers
91 views

Periodic sequence with exponentially increasing period?

I have to develop a physical model for a certain type of biological oscillation that can be built upon periodic sequences. From earlier questions I know that any periodic sequence (containing $0$s ...
1
vote
0answers
332 views

Normal modes of oscillation: how to find them

Are normal modes the eigenvectors of the matrix $(\omega ^2 T- V)$ where $T$ is the matrix of kinetic energy and $V$ is the matrix of potential energy? Is it the only way to express them? How can I ...
1
vote
0answers
157 views

Conveyor scales modeling

Assume we have a conveyor scales. Which consists of scales, and motor with conveyor belt placed above, so that the boxes can be measured (weight) while moving above. What I want is to create the model ...
0
votes
0answers
18 views

Amplitude resonance

Why does amplitude resonance occur at a frequency lower than the natural frequency of a body? specifically, why is $w=\sqrt{w_0^2-2a^2}$ where $a=\frac{damping\space force}{2\cdot mass}$
0
votes
0answers
44 views

Entropy of an oscillator in Einstein's solid

This is a homework problem and I need help with it. A solid's (Einstein's model) oscillators are in the first excited state on average. How much entropy does one oscillator have? What I've tried so ...
0
votes
0answers
52 views

Transfer Equation between two oscillating pendulum collision

How to model the energy transfer equation between two oscilators colliding? For example two pendulum oscilating at frequency $f_1$ and $f_2$ and they transfer energy during colision.
0
votes
0answers
80 views

Coupled Oscillation Simulation

I'm looking for an online coupled oscillation simulation. The best I have got so far is this --- https://phet.colorado.edu/sims/normal-modes/normal-modes_en.html But I'm looking for something which ...
0
votes
0answers
84 views

More on the closed-form for a simple pendulum

I've learnt about the simple pendulum, and while the regular curriculum only uses the linear approximation of $\sin\theta$ to obtain $\ddot\theta+\omega_0^{2}\theta=0$. I tried to find out about a ...
0
votes
0answers
59 views

Mass frequency problem

For Dispersion relation , according to Gaussian profile, the author in the equation 3 wrote as $\omega= \left(k^2+\omega_{mass}^2\right)^{1/2}$ My question is what is mass frequency and how it arose ...
0
votes
0answers
199 views

Coupling oscillator

I am currently doing the following problem: Two identical undamped oscillators, A and B, each of mass m and natural (angular) frequency $\omega_0$, are coupled in such a way that the coupling ...
0
votes
0answers
191 views

Determining the length of a Torsional Pendulum

Currently working on this question, however I'm not sure how to solve it. As a pendulum swings in simple harmonic motion at the surface of the Earth, the angle the pendulum makes relative to its ...