Questions tagged [oscillators]

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Damped oscilator - logarithmic decrement of damping [closed]

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 ...
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1answer
276 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 ...
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1answer
124 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
2k 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
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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
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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 ...
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0answers
421 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
681 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? $$m\dfrac{d^2x}{dt^2}=F=-\dfrac{dU}{dx}=-3kx|x|.$$ ...
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2answers
281 views

Approximations in simple pendulum

In the approximation $$-(g/ \ell) \sin \theta \approx -(g/ \ell) \theta $$ we make an error $R$ which is $O(\theta ^3)$. If i did well my calculations it is estimated by $$R\leq|(g / \ell)(\theta^3/3!)...
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1answer
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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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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
5k views

Can a simple pendulum be considered a simple harmonic oscillator?

Is the motion of a simple pendulum, a simple harmonic motion? It stops vibrating after sometime.
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3answers
493 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 ...
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3answers
840 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..
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1answer
330 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 ...
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1answer
4k 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 ...
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4answers
28k views

Phase difference of driving frequency and oscillating frequency

Suppose 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' oscillation frequency. However I'm told that the phase ...
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0answers
814 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 ...
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2answers
292 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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3answers
406 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?
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3answers
45k views

Does the human body have a resonant frequency? If so, how strong is it?

Inspired by this question on Music beta SE, I'm wondering if the human body has a strong resonant frequency. I guess the fact that it's largely a bag of jelly would add a lot of damping to the system, ...
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1answer
1k 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 ...
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105 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 ...
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1answer
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How the frequency of the oscillation is affected?

Is the frequency of oscillation of a rotating disk affected if a mass hanging from (attached to the disk but pulled by gravity) the disk exerts a torque on the rotating disk?
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2answers
675 views

Why do joined massless springs, act like a rope under tension?

In an oscillations exercise there is a spring attached to another spring, attached to a block. Long story short: I have to find the global $k$. In the solutions it says: "Because the springs are ...
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3answers
3k views

How does energy depend on frequency in an alternating current circuit?

In what relation is the energy input in an alternating current circuit to its frequency? I'd guess I have to compute something like $$E=\int P(\omega,t) dt=\int U(\omega,t) I(\omega,t) dt, $$ but ...
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Springs yet again, this time with a picture. Infinite displacement, makes no sense [duplicate]

Possible Duplicate: How could this damped oscillator ever go to infinity? Or negative infinity for that matter? Consider this http://img854.imageshack.us/img854/1391/78679184.jpg! Where I ...
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2answers
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How does the Milkovic Two-Stage Mechanical Oscillator Pendulum-Lever System work?

See http://peswiki.com/index.php/Directory:Milkovic_Two-Stage_Mechanical_Oscillator The Two-Stage Mechanical Oscillator Pendulum-Lever System is very simple, yet very puzzling because it appears ...
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3answers
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When are Maximum Velocity and Acceleration acheived in Simple Harmonic Motion?

Im trying to get my head around SMH out of curiosity because it seems simple yet I'm not getting the concept behind some ideas. For a SMH equation : $$ x=a \sin(\omega t+\phi) $$ Under what ...
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1answer
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Finding phase angle of simple harmonic motion [closed]

A sinusoidal oscillator has : $$x=x_{max} \cos(\omega t - \varphi )$$ Period is 2, initial displacement is 100mm initial velocity is 200mm/s What is the phase angle assuming $-\pi < \varphi < ...
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2answers
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How could this damped oscillator ever go to infinity? Or negative infinity for that matter?

This is an ODE problem,but I cannot visualize why it can go to infinity or negative infinity. Consider $$x'' -6x' + 8x = 0$$ Where $x''$ is acceleration, $-6x'$ is the damping effect and $8x$ is ...
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1answer
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What makes up a resonator of radio?

I was reading this article about resonators. Quote: The sine wave that matches that particular frequency will get amplified by the resonator, and all of the other frequencies will be ignored. ...
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3answers
422 views

Quality factor for a quantum oscillator?

I've been reading papers about nanomechanical oscillators, and the concept of quality factor often pops up. I understand to some extent about Q factor in classical sense, but since nanomechanic ...
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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 ...
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Will a violin string keep vibrating for a longer time in vacuum than in air?

Hitting a string of a violin or a guitar will cause that string to vibrate, but after short time the amplitude of the vibration will decay, consequently the produced sound will die out. I suppose ...
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What's a good textbook to learn about waves and oscillations?

I'm taking a course on waves and oscillations using Crawford from the Berkeley series (out of print excluding international copies), and would like to know if anyone has any suggestions for a better ...
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1answer
3k views

How does the X-Y mode of an oscilloscope work?

I recently used an oscilloscope in X-Y mode to draw the phase ellipse of two voltages. I then used the formula $\phi = \arcsin(2y/B)$ where $y$ is the value of the ellipse at $x = 0$ and $B$ is the ...
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645 views

Conservation of energy in a non-linear oscillator

I have a homework question about a "non-linear oscillator". I actually have an answer to this question, but the answer I get is stronger than what is needed according to the question. The question ...
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1answer
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Help understanding this forced undamped oscillator

I have a forced oscillating system, with driving force as $f_0\cos\omega_0 t \cos \delta t$ giving the equation of motion: $$\ddot{x}(t) +\Gamma \dot{x}(t) +\omega_0^2x(t) = f_0\cos\omega_0 t \cos \...
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How do I solve for the phase constant given the amplitude and the angular frequency?

A piston (with mass M) in a car engine is in vertical simple harmonic motion with amplitude A. The engine is running at a period T. Suppose a small piece of metal with mass m were to break loose ...
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1answer
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Numerical computation of the Rayleigh-Lamb curves

The Rayleigh-Lamb equations: $$\frac{\tan (pd)}{\tan (qd)}=-\left[\frac{4k^2pq}{\left(k^2-q^2\right)^2}\right]^{\pm 1}$$ (two equations, one with the +1 exponent and the other with the -1 exponent) ...
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2answers
626 views

Wave equations & propagation theories

I'm interrested in making computer simulation but I've run into rather physics oriented problem. I have to choose how to propagate my wave. Though I've found technique called FDTD (finite-difference ...
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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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Quantum shot-noise and the fluctuation dissipation theorem

Classically, shot noise observed in the signal generated by a laser incident on a photodiode is explained as being due to the quantization of light into photons, giving rise to a Poisson process. In ...