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52 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 ...
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3answers
128 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 ...
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2answers
539 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 ...
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1answer
4k 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 ...
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3answers
141 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 ...
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1answer
42 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 ...
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0answers
251 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= ...
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1answer
110 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
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1answer
124 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 ...
10
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1answer
416 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
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2answers
316 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, ...
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0answers
61 views

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

How to derive the equation in my question?
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2answers
132 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?
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2answers
139 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 ...
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3answers
800 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
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1answer
498 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 ...
1
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1answer
259 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
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1answer
39 views

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

Does temperature have an influence on the frequency of an oscillating organ pipe?
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0answers
57 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 ...
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0answers
186 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
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1answer
165 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
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1answer
79 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 ...
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0answers
85 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 ...
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2answers
247 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
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1answer
287 views

Applications to the Van der Pol equation? [closed]

What are some applications to the Van der Pol equation? Are there any physical examples?
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2answers
91 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 ...
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1answer
149 views

Would a truly physical oscillation still be measured in hertz?

I recently bought a new scroll saw and was commenting to someone about how it was a relatively slow saw... low ... RPMs (thinking like a circular saw). Then it occurred to me that not being a circle, ...
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1answer
2k views

Does a guitar sound different in zero (or micro) gravity?

Seeing a video of astronaut Chris Hadfield playing a guitar on the International Space Station made me wonder if a guitar or other stringed instrument played in zero-G would sound any different than ...
3
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2answers
220 views

Probability of position in linear shm?

The problem that got me thinking goes like this:- Find $dp/dx$ where $p$ is the probability of finding a body at a random instant of time undergoing linear shm according to $x=a\sin(\omega t)$. ...
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0answers
179 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 ...
0
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1answer
378 views

Damped oscilator - logarithmic decrement of damping

Could you please tell me, where is the mistake? What is the logarithmic decrement of damping $Λ$ of damped harmonic oscillator, if its mechanical energy decreases to the 50% of its initial value ...
0
votes
1answer
118 views

Harmonic oscillator with light damping

My textbook gives the following for x as a function of time for a lightly damped harmonic oscillator: $$ x = Ae^{- \gamma t} \cos (\omega \, t)$$ for $\gamma = \dfrac b {2m}$. It says this implies ...
0
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1answer
80 views

Pendulum system: how is derived the output as Energy?

Good day to everyone, I want to understand in which way the "Energy equation" is been implemented to this pendulum system. $x_1(t)$: The angular position of the mass $x_2(t)$: The angular velocity ...
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1answer
342 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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1answer
983 views

Standing Waves: finding the number of antinodes [closed]

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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2answers
1k views

Calculating phase difference of sound waves

An observer stands 3 m from speaker A and 5 m from speaker B. Both speakers, oscillating in phase, produce waves with a frequency of 250 Hz. The speed of sound in air is 340 m/s. What is the phase ...
4
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0answers
120 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 ...
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3answers
236 views

Non-SHM oscillatory motion

How to solve these kind of questions , where $|F| \propto x^2$? How to find time period and velocity type related things to the oscillatory motion? ...
3
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1answer
383 views

Simple pendulum period in three different cases

Imagine you have a simple pendulum hanging on the ceiling of a train which has a period called T. How will the period be in the following cases: When the train is in circular motion in a curve of ...
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3answers
1k views

What is the period of a physical pendulum without using small-angle approximation?

What is the expression for the period of a physical pendulum without the $\sin\theta\approx\theta$ approximation? i.e. a pendulum described by this equation: $$ mgd\sin(\theta)=-I\ddot\theta $$ ...
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2answers
577 views

Why is simple harmonic motion called so?

Is the motion of a simple pendulum, a simple harmonic motion? It stops vibrating after sometime.
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2answers
253 views

Motion of a pendulum

The equations of motions for a simple pendulum is given by $$\ddot{\theta} ~=~ -\frac{g}{\ell}\sin(\theta),$$ where $g$ is acceleration due to gravity and $\ell$ is the length of the pendulum's ...
2
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3answers
214 views

Condition for closed orbit [closed]

I'd like to know when an orbit is closed. I know that, to have a closed orbit, there is a ratio that must be a rational number, but I don't know other things..
3
votes
1answer
137 views

Why don't we use quater-circular dees instead of semi-circular dees in a Cyclotron

This is the setup, I have in my mind: O1, O2, O3 and O4 are 4 oscillators. The arrows in between the Dees represent the alternating EMF the Oscillators will generate. I think we can easily adjust ...
2
votes
1answer
787 views

How do I account for the direction of friction acting on a spring?

I would like to set up the equations of motion for a simple spring oscillator. Let's have a spring lying horizontally; we attach a small mass $m$ to the (massless) spring. The force of the spring ...
2
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2answers
4k views

Phase difference of driving frequency and oscillating frequency

If a mass is attached to a spring and is oscillating (SHM). If a driving force is applied it must be at the same frequency as the mass's oscillation frequency. However I'm told that the phase ...
1
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0answers
300 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 ...
3
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2answers
201 views

“Inverted” quantum oscillator

I'm trying to understand the problem of the "inverted" oscillator, which has the following Hamiltonian: $$ \hat{H}=\frac{\hat{p}^{2}}{2m}-\frac{k\hat{x}^{2}}{2} $$ Suppose that a particle at the ...
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2answers
190 views

Small Oscillations and matrices: suggestion about text

I'm undergraduate and I'm looking for a text about Small Oscillations in which matrices are used. Could you suggest me a book or a PDF file?
1
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1answer
371 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 ...