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2
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1answer
101 views

Tuned Mass Damper

I was learning about the different applications of resonance and one of them is the tuned mass damper used in buildings. One thing I am confused about is as to why the mass attached to the building ...
17
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8answers
2k views

Why are sine/cosine always used to describe oscillations?

What I am really asking is are there other functions that, like $\sin()$ and $\cos()$ are bounded from above and below, and periodic? If there are, why are they never used to describe oscillations in ...
0
votes
1answer
183 views

Does sound absorption depends upon the amplitude of sound wave?

I can understand the mechanism of frequency dependant sound absorption by most materials but does the sound attenuation also depends upon the AMPLITUDE(sound pressure or rather loudness/sound ...
0
votes
0answers
94 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
1answer
123 views

Derivation of Foucault pendulum [closed]

Let us define our usual Cartesian coordinates ($x'$,$y'$,$z'$), and let the origin of our coordinate system correspond to the equilibrium position of the mass. If the pendulum cable is deflected from ...
1
vote
0answers
71 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
47 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
3answers
42 views

What are the means to consider that a specific function is phase of an oscillator?

I hope the experts of the field forgive me for this n00b questions, but I am just trying to understand physics. Assume the following function: $$\phi(t)=\omega t+\cos(\omega t)$$ The above function ...
8
votes
2answers
3k views

What creates the chaotic motion on a double pendulum?

As we know, The double pendulum has a chaotic motion. But, why is this? I mean, the mass of the two pendulums are the same and they have the same length. But, what makes its motion random? I'm just ...
2
votes
2answers
385 views

Harmonic Oscillator driven by a Dirac delta-like force

Consider that there is no damping for simplicity. As we know, a driving force of the form $\sin(\omega t)$ will make the oscillator at steady state vibrates at the external frequency $\omega$. What ...
1
vote
1answer
58 views

Why can we use the energy of a pendulum to calculate its frequency?

The question might sound rather vague; to calculate the frequency using the energy we simply use that the total energy is constant, set the derivative to zero and solve the equation of motion that ...
8
votes
1answer
218 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
2answers
165 views

Energy of a damped oscillator

$$ E=\frac{1}{2}m\left(\frac{dx}{dt}\right)^2+\frac{1}{2}m\omega_0^2x^2. $$ This is the equation for the energy of a oscillator. The second term is the potential energy. Now, my question is, will ...
4
votes
2answers
159 views

Definition of quantum anharmonicity

I have been reading research papers in mathematical physics for some months now, and I've seen the the term "anharmonic oscillator" quite frequently. At first I assumed that given a Schrodinger ...
2
votes
1answer
229 views

Principle of Superposition for driven oscillator

So I understand the the Superposition Principle states that all the forced oscillations, as determined by multiple external forces, are to be added up in order to get the entire solution. However, ...
3
votes
1answer
245 views

Is using a swing an example of normal or of parametric resonance?

Parametric resonance is a situation where the driving frequency is a multiple of the eigenfrequency. Various people say that using a swing and propelling it oneself is such a case, with the driving ...
2
votes
1answer
426 views

Synchronizing Pendulums

Assume we have a frictionless pendulum of length $l$ with mass $m$. This pendulum hangs from some weightless contraption, which is itself bolted to a platform. This platform can move horizontally in ...
0
votes
1answer
101 views

How to include Damping in a Simple harmonic oscillator

Im designing a model for Kelvin Method. Some of my calculation results are as follows: Radius of the membrane : 50 micron thickness of the membrane : 3.25 micron resonate frequency : 1.32MHz ...
0
votes
1answer
146 views

Oscillator, angular frequency equation

I found the highlighted equation on the Wikipedia on angular frequency, however it doesn't say how it was obtained, could someone please explain that? Also, it says that the spring is massless, if ...
4
votes
2answers
128 views

How can I find the amplitude?

Prove that the motion of a mass $m$ on a linear spring with constant $k$, has the form $$y (t) = A \sin(wt+f),$$ where $t$ is the time and $A, w, f$ are constants. We know that for $t = 0, y(0)=y_{0}$ ...
1
vote
1answer
34 views

Lagrangian Oscilattor

I want to know how to calculate the normal modes from a Lagrangian. I make the T (kinetic energy matrix) and U (potential energy matrix), and then I calculate the determinant of $|T-\omega ^2 U|$ ...
2
votes
1answer
191 views

Nature of motion of a pendulum

Consider a pendulum suspended from the ceiling of a lift in free fall , if its displaced from its mean position , what will be its nature of motion? what i thought was that it would simply stick to ...
3
votes
2answers
873 views

Oscillation of a rolling sphere in a bowl [closed]

This is a homework task. I already came to a result but I am very unsure. The task: In a bowl with the shape of a semi-circle ($R$ = 0.5m) a sphere (there is no specification for the size of the ...
2
votes
1answer
95 views

Neutrino mass and energy question

If a neutrino has mass then it travels less than the speed of light. Suppose I boost myself to the rest frame; i.e. bring it to rest in the laboratory. Now if it oscillates between different states ...
0
votes
1answer
218 views

Oscillation Question [closed]

Now normally (if it was a block not rotating) all you would have to do is use $w^2 = k/m$ and $E= \frac12k(A\cos(2wt+\theta))^2 + \frac12m(Aw\sin(wt+\theta))^2$ or in other words the translational ...
1
vote
3answers
228 views

Why do degenerate normal modes appear as complex conjugate pairs?

Can anyone prove this? THE DETAILS Suppose we have a system with n components, (i.e. $|~{\psi}(t)\rangle=\sum \langle x_i|~\psi(t)\rangle ~|~x_i\rangle$) where our equation of motion is described ...
0
votes
2answers
1k views

What are “correlation time” and “relaxation time” in oscillations?

I am reading this paper which is about oscillations. I came across two terms called "Correlation time" and "Relaxation time" in the following passages: In this Letter, we solve these problems by ...
0
votes
1answer
22k views

How to find the phase constant? [closed]

I was given this velocity-vs-time graph of a particle in simple harmonic motion: I determined the amplitude to be $A = 1.15$ m, which Mastering Physics confirmed is correct. Then I was asked to ...
4
votes
3answers
157 views

What is the meaning of $U''(x)=0$?

Most potentials with a minimum can be described approximately as a harmonic oscillator. So the procedure is to Taylor expand $U(x)$: $$U(x)=U(0)+U'(0)x+\frac{1}{2}U''(0)x^2 +...$$ If we suppose ...
3
votes
1answer
64 views

Neutrino flavor eigenstate interaction with matter

We know that neutrino eigenstates are not mass eigenstate and this therefore produces neutrino oscillations. This is, however, deduced from the fact that the neutrino of one flavor produces the ...
1
vote
0answers
404 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
1answer
306 views

Normal Coordinates for Quantum Coupled Oscillators

Thanks if you take the time to read this. Here is the problem statement: The problem I'm getting is that I'm not getting the kinetic energy diagonal when I convert to the coordinates that ...
1
vote
2answers
239 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 ...
12
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2answers
609 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
443 views

Rabi oscillations and two level dynamics

I'm currently looking at Rabi Oscillations, and not I have a look at the following equations: $$W = \sqrt{\Omega^2+\delta^2}.$$ The amplitude: $$\frac{|\Omega|^{2}}{\delta^{2}+|\Omega|^{2}}$$ Now, ...
0
votes
0answers
65 views

How to derive the equation in my question? [duplicate]

How to derive the equation in my question?
3
votes
2answers
209 views

Linearized equations

What is $V_{\alpha\beta}$? And what is a symmetric, positive definite potential energy matrix? And why is there a linearized equation like this?
1
vote
2answers
206 views

Period $T$ of oscillation with cubic force function

How would I find the period of an oscillator with the following force equation? $$F(x)=-cx^3$$ I've already found the potential energy equation by integrating over distance: $$U(x)={cx^4 \over ...
1
vote
3answers
1k views

Frequency of small oscillation of particle under gravity constrained to move in curve $y=ax^4$

How to find the frequency of small oscillation of a particle under gravity that moves along curve $y = a x^4$ where $y$ is vertical height and $(a>0)$ is constant? I tried comparing $V(x) = \frac ...
2
votes
1answer
855 views

What is the amplitude of the limit cycle of the van der Pol oscillator?

In the second edition of Classical dynamics of particles and systems by Jerry B. Marion, it is said that the van der Pol equation $$\ddot{x}-\mu\left({x_0}^2-x^2\right)\dot{x}+{\omega_0}^2x=0$$ where ...
2
votes
1answer
428 views

Coupled Oscillators

This is an exercise of my last exam. Since I couldn't find anybody who solved it or knows how to, it would be really nice if somebody could tell me if my thoughts on it go into the right direction. ...
2
votes
1answer
40 views

Organs & Oscillations: An Analysis on the Temperature Dynamics of Solids

Does temperature have an influence on the frequency of an oscillating organ pipe?
0
votes
0answers
64 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
272 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 ...
2
votes
1answer
306 views

What is the phase difference of the oscillations of the two prongs of a tuning fork? [duplicate]

What is the phase difference of the oscillation of a tuning fork?
1
vote
1answer
114 views

Duhamel formula for propagators

Let $\dot{z} = A(t)z + b(t)$ with $ z(t) \in \mathbb{R}^n$ and $A(t)$ be a linear map from $\mathbb{R}^n \rightarrow \mathbb{R}^n$. A propagator is also a linear map $P(t,s):$ $\mathbb{R}^n ...
1
vote
0answers
106 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
2answers
362 views

Oscillation with exponentially increasing period

I am trying to build a model for a certain type of oscillatory behaviour with a kind of exponential dilatation. How can I modify the function of a simple cosine oscillation $\psi(x)=A_0 \cos(2\pi\; ...
0
votes
1answer
510 views

Applications to the Van der Pol equation? [closed]

What are some applications to the Van der Pol equation? Are there any physical examples?
5
votes
2answers
108 views

Is it possible to find a “replacement pendulum” for a system of two equal but perpendicular pendulums?

I ask this question, because at the end of this long day I'm just too dazed to derive the proofs myself (even though I know that I should feel ashamed for this). So, the question: Given two ...