Questions tagged [oscillators]

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5
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423 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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0answers
3k 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 = \...
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1answer
306 views

Does electron have some intrinsic ~$10^{21}$ Hz oscillations (de Broglie's clock/Zitterbewegung)?

Louis De Broglie has postulated in 1924 that with electron's mass there comes some $\approx 10^{21}$Hz inner oscillation: $E=mc^2=h f=\hbar \omega$. We would get such oscillation e.g. if using $E=mc^...
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1answer
255 views

Damped quantum harmonic oscillator - evolution of coherent state

I am trying to solve the following Master equation (also similar to damped quantum harmonic oscillator): $$\frac{d\hat{\rho}}{dt} = \frac{\Gamma}{2}\left(2\hat{a}\hat{\rho}\hat{a}^{\dagger} - \hat{a}^...
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1answer
79 views

Swing: why does the body position modify the amplitude?

When a person swings, why does the amplitude of oscillations increase if the person changes the body position ? That is, when descending and approaching the vertical position, if the person extend his ...
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0answers
51 views

If a hollow sphere connected to a rope and half-filled with water forms a physical pendulum, what does the water surface do?

Suppose I make a pendulum consisting of a long string connected to a hollow sphere, then fill the sphere half way with water and set the pendulum in motion by giving all the water and the sphere some ...
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0answers
55 views

Prove from first principles that a guitar string will vibrate at a constant frequency

From experience I am aware that a taught string will generally vibrate with a constant frequency. I wanted to prove this by considering the relation of distance from the resting position, and its ...
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0answers
702 views

What is the mechanism of subharmonic oscillations?

It's clear to me from linear systems theory that energy manifested within a fundamental mode of resonance can saturate with the excess energy spilling over into harmonic frequencies greater than the ...
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23 views

String conservation with springs

I was trying to solve this Problem that asked to find the period of small oscillations for this system. To do so I used the fact that for a massless pulley with strings around it, the sum of the ...
2
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3answers
79 views

Oscillator with decaying restoring force

Suppose a system that is described by the equation of motion: $$ \ddot{x} = -k\cdot x\cdot \exp\left(-\frac{t^2}{2\sigma^2}\right). $$ (For example a spring with decaying stiffness.) I'd like to ...
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1answer
345 views

How resistance in coils affects the damping of oscillations of a magnet through them

I performed an experiment where I connected a magnet to the end of a spring with the north side on the bottom. The magnet at the tip of the coil was aligned to pass through a column of coils of about ...
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2answers
36 views

Oscillation period of a hard stick hung at both ends

Hi all, Does anyone know how this set-up will affect the oscillation period of the system? We have been measuring using timer and this set-up always yields longer period than standard pendulum ...
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0answers
91 views

Massless Electrons and Effect on Graphene Mass

I've read that electrons in graphene can travel masslessly, due to the effect of the graphene crystal around them. I'd also read that the application of an electric field can change this behavior and ...
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0answers
98 views

Solvable model with harmonic oscillator

I need help with a mathematical physics question. I have given the following system: A spin is coupled to a single harmonic oscillator mode with Hamiltonian $$H=(\epsilon/2) \sigma_{z} + \omega\, a^{...
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0answers
426 views

What is the difference between “normal mode” and just “mode”?

So in the oscillation problems, is there difference between "mode" and "normal mode"? I know that "normal modes" are independent and orthogonal, so one doesn't affect the other. Now I am not sure when ...
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3answers
591 views

Entropy of environment of pendulum?

I remember reading a statement along the lines of: Suppose our system is a simple pendulum. Then the entropy change in it is overall zero because the system is periodic. However, the entropy of ...
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0answers
96 views

Electrical circuit analogue of a nonlinear pendulum

Is it possible to make an electrical circuit analogue of a nonlinear pendulum? To model the equation $$y'' = -\sin(y)$$ They did this on analog computers in the past, but how? How to model the ...
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0answers
42 views

Coulomb's static friction in multidimensional case - decide which mass begins to move

Consider a system of N coupled oscillators, under the effect of elastic forces, damping, dynamic and static friction and an external force; for simplicity, let's suppose $N=3$. The friction model is ...
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0answers
24 views

References on particle cooling

I am looking for references on the topic of particle and mechanical oscillators cooling, in particular: Doppler cooling Resolved sideband cooling and Lamb-Dicke regime Stokes and anti-stokes modes ...
2
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1answer
124 views

Analysis of motion of a body moving on a string?

I was wondering about something I observed yesterday. To give some background, one of my hobbies is slacklining. This is essentially like tight-rope walking but with a one inch piece of (in this case ...
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0answers
106 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 ...
2
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1answer
206 views

Simulation of oscillator with frequency dependent damping

What would be the equation for the frequency dependent damping of harmonic oscillator? Is there something like: $$ \ddot{x}+2\delta\dot{x}+\omega_0^2x = \frac{F}{m}f(t) $$ with frequency dependent ...
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36 views

External force in the Navier-Stokes momentum equation

The Navier-Stokes momentum equation is $$ \rho\frac{\partial \bf{v}}{\partial t}+\rho(\bf{v} \cdot \nabla\bf{v})=-\nabla P + \nabla\cdot \bf{\tau} +\bf f $$ where $\tau$ is the deviatoric stress ...
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0answers
33 views

Why is water in the asymmetric cylinder not capable of Simple Harmonic Motion?

I'm learning physics in a high school. I'm curious why water in the asymmetric cylinder is not capable of SHM. I've learned that water in a symmetric cylinder can make a Simple Harmonic Motion. But ...
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42 views

Analytical solution to damped harmonic oscillator - Fokker-Planck equation

In the paper "Numerical solution of two dimensional Fokker-Planck equations" (available at: https://doi.org/10.1016/S0096-3003(97)10161-8), the authors quote an analytical solution to the damped ...
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0answers
46 views

3D harmonic oscillator magic numbers

I know that, $$V(r) = (1/2) m \omega^2 r^2 ,$$ $$\omega \approx 40(Z+N)^{-1/3}\ \rm{MeV} $$ and $$E = (n+3/2) \hbar \omega.$$ How do you find the magic numbers of protons and neutrons which ...
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2answers
281 views

Difference between Oscillatory motion and vibratory motion

What is the difference between oscillatory motion and vibratory motion. I have read in my book that "If the amplitude of oscillatory motion is extremely small,the motion is called vibratory motion". ...
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0answers
43 views

Resonance and energy flow

In this post, Alfred Centauri describes the resonance as a phenomenon which appears when 'the energy flow from the driving source is unidirectional' and then shows that this is the case for $\Omega=\...
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0answers
29 views

Spring oscillation model

When a spring - in real world - is extended $Xo$ from its natural position, it oscillates and eventually decreasing it's amplitude with time, comes to a stop. Is this a damped system or no? If yes how ...
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53 views

How to evaluate the period of a particle in a system with potential energy $U=-U_0/\cosh^2(\alpha x)$?

I am working through the textbook "Mechanics", from the series "Course of Theoretical Physics " by Landau and Lifshitz. In Chapter 3, where the authors talk about integrating the equation of motion $E=...
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1answer
83 views

Finding the Amplitude of a Spring Oscillation given initial Position and Velocity

I'm trying to create a physics simulation, and I need to be able to determine the amplitude of the oscillation of a mass-and-spring system given any position that the mass might be in and the velocity ...
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70 views

Spring with oscillating support (Goldstein chapter 11, problem 2)

The problem: A point mass m hangs at one end of a vertically hung hooke-like spring of force constant k. The other end of the spring is oscillated up and down according to $z=a\cos(w_1t)$. By ...
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3answers
88 views

$Q$-factor for damped oscillator (not driven)?

How would this be defined? Some of the Q-factor definitions I have encountered include: $$Q=2\pi\frac{Energy \space stored}{Mean \space power \space per \space cycle}\\Q=2\pi\frac{Energy \space ...
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1answer
46 views

Forced Oscillations and Complex Representation

An oscillating force $F \cos \omega t = \Re\{Fe^{i\omega t}\}$, where $F$ is real, is applied to a mass $m$ on the end of a spring with spring constant $k$. The displacement, $x$, of the particle can ...
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2answers
166 views

Is the equation of motion for a spring-damper system the same whether oriented upward or downward?

So every spring-damper system I've found online has the equation of motion: $$mx''+cx'+kx=0$$ I can understand how this is derived when downwards is positive, but what about when upwards is ...
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0answers
19 views

Generate oscillation (approx. f=50 HZ, Ampl=20 MikroMeter )

I want to adapt the height of a sample under a microscope. I have an x-y-positioner but no z-positioner. As a x-y-z-positioner is too expensive (about 16 k €) I want to build an own solution. First ...
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0answers
41 views

Why is an imaginary impedance compenent frequency dependent in a circuit?

And can we have a real frequency-dependent component or constant imaginary component to an impedance? My thoughts on the first question are that, an imaginary component to the impedance does not ...
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1answer
267 views

How does a gyroscope flip?

Consider a gyroscope which is hanging with a string. Is it possible to $flip$ the orientation of the a gyroscope by oscillating the point of suspension? How does it come out mathematically?
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0answers
30 views

What factors affect opposite pole bouncing

I have two magnets with holes on a stick, and when the like poles are adjacent the upper magnet floats. When the upper magnet is held against the lower and then released the top magnet flies off and ...
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0answers
214 views

Deduce transfer function in a mechanical network

I am familiar with a 2 degree-of-freedom (2DOF) system like it is depicted here: Assume all parameters are unknown. Now, how do I find the values of the parameters in case of A) a spring and ...
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1answer
111 views

At what height will the tension of the string attached to a bob which was given an initial velocity from the bottom become zero?

Assuming a bob attached to a string is given a horizontal velocity u when it is at the bottom, what would be the height at which the tension of the bob would be zero (i.e the bob leaves the circular ...
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1answer
185 views

Oscillation of mass $m$ on a spring when another mass $m$ is added to it at equilibrium

I have a spring of length $L$ when unstretched with one end fixed to the roof. At the lower end I place a mass $m$ and drop gently so it stretches by $x_1$ at equilibrium so that $mg=kx_1$. Now I ...
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0answers
91 views

Frequency of an underdamped driven oscillator

Let a particular solution of the differential equation $$\ddot{x}+2\gamma \dot{x}+\omega_0^2 x=\sum_{n=-\infty}^{\infty}c_n e^{i n \omega t}$$ be given by $$x=\sum_{n=-\infty}^{\infty}\frac{c_n}{2\...
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1answer
227 views

Determination of spring constant $k$ for an elastomer

Primary Question: How can you determine the spring constant $k$ of an elastic material? I was recently tasked with finding the spring constant for a series of elastomeric materials, the first of ...
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0answers
108 views

Oscillating waves on a water stream

I observed something which I've never seen before. We left the tap open and the water stream was flowing in a particular pattern. When we placed a beaker under the water stream, the pattern ...
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1answer
312 views

Triangle swinging around a pivot

im studying oscilatory motion, and i have a problem that asks me for the angular frequency of a group of sticks,each stick has mass M and length L, that form an equilateral triangle swinging around a ...
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0answers
211 views

Equations of motion for a torqued spherical pendulum

I Want to simulate a spherical pendulum with a torquer on it, i.e. the angles of the pendulum change not only due to torque generated by gravity, but also by a torquer attached to the top of the ...
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0answers
371 views

Differential equation for an accelerometer

I am having troubles deriving the 2nd order differential equation for the system below, where $r=y-s$. According to my lecture notes the differential equation is $$ M\frac{d^2r}{dt^2}+b\frac{dr}{dt}+...
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0answers
418 views

Phase plane of simple pendulum

I'm trying to create a phase plane of simple pendulum motion by plotting $\dot\theta$ against $\theta$ in Matlab. I have the equation $\ddot\theta + \sin\theta = 0$, then by integrating I come to the ...
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1answer
58 views

Predicting the behaviour of a spring-mass system under the influence of regular periodic impulses

Here is the question: I have a mass 'm' connected by a spring to a wall. The setup is horizontal. The time period of the mass is 'T0' determined by the spring constant 'k'. The mass obeys a position ...