Questions tagged [vibrations]
The vibrations tag has no usage guidance.
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How can you change the resonant frequency of a solid guitar body?
I am trying to figure out if it would be possible to change the resonant natural frequency of a solid-body guitar. For example, let's say it resonates at 100 Hz and I want it to resonate at 200 Hz. Is ...
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Inconsistent units in modal analysis of vibrating beam
(read the last sentence for the actual question).
Consider an elastically suspended solid body from a massless cantilever beam
The equations of motion of such a system are
$$\begin{bmatrix}m\\
& ...
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Create a plausible vibration signal from a sliding RMS window
So lets say I have observed many vibration signals and build a sliding window of the RMS of said vibration signals as well as other statistical measurements such as the variance and nth order ...
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Does air column change its frequency to one of its modes as and when needed?
The question might make it sound like I'm considering air column to be a conscious entity kinda thing, but what I really mean is,
Say I've a tuning fork ringing and I bring it near a test tube with ...
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Calculate the Frequency of Clamped Bar
I'm trying to calculate the resonant frequency of a clamped bar or rather I'm trying to calculate what length of bar to use to get a certain frequency. The goal is to be able to use this to make ...
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What causes this strange noise in a pair of walkie-talkies?
Let us suppose that Bob and Alice both have walkie-talkies. They are both 3m apart from one another. Alice pushes her walkie-talkie to speak but instead of speaking, she starts walking toward Bob. ...
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Raman scattering collection geometry
I believe that most Raman spectroscopy measurements are carried out with the collection optics being at either 180$^{\circ}$(back-scattering) or 90$^{\circ}$ from the excitation source. Are there any ...
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Motion of non-homogeneous string fixed at both ends when pulled at a point
How to solve displacement and velocity profile of string which has density $d_{1}$ till distance $x$ and density $d_{2}$ from $l - x$ to $x$ fixed at both ends and when given initial displacement and ...
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Determining the equations of motion for a 2 DOF in 2 directions
I'm having trouble understanding a 2DOF system that moves in 2 directions. The problem asks me to determine the EOM for a system shown in the attached image:
My first idea is to transform this system ...
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Can you measure mass using an accelerometer?
Is it possible to use an accelerometer and a microcontroller to measure mass of an object up to 500g. These two electronics would be attached and be portable.
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Expression for Steady state of Forced vibration [duplicate]
In my book under the topic Steady state of the forced oscillator, they started with the equation:
$$\frac{d^2x}{dt^2}+γ\frac{dx}{dt}+ω_0^2x=fe^{jωt}$$
I know the equation for damped oscillation but it ...
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Why does plucking a string produce harmonics instead of a pulse?
If I jerk a wire from the free end fixed at an end and then fix the free end, it will produce a pulse travelling back and forth between the two ends. So in a string fixed at both ends, if we pluck it ...
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How to derive specific heat of a crystalline material from phonon density of states?
I have done a simulation of a crystalline material using DFT and have extracted its normal modes and its phonon density of states.
Does anyone have an algorithm/code or a detailed resource that can ...
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How do I deal with rigid body mode shapes of an MDOF system?
I'm trying to solve a vibrations problem for an MDOF system (3 DOF) where I need to determine the natural frequencies and mode shapes. I found all three frequencies by finding the eigenvalues (w=sqrt(...
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How can oscillations be there with constant voltage source in RLC circuit?
In this video the professor closes the switch at $t=0$ and the circuit produces damping oscillations(charge) before settling to a steady value. How is it possible?
I understand the oscillations in LC ...
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Do all particles oscillate with same frequency in a crystalline solid?
For the reference : lecture notes
In the derivation for the displacements in an oscillating monoatomic crystal the notes assume an $\omega$ (angular frequency) and $k$ ( wavenumber) that is the same ...
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What is the reason that the vibrating body gradually acquires the frequency of the external periodic force in forced vibration?
When an external periodic force is applied on a vibrating body the body no longer vibrates with its own natural frequency but it gradually acquires the frequency of the applied periodic force.
I don'...
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Free response of plucked string
Based upon points $x=l/4$ and $x=l/2$, how would one determine the relative error between the free response at $t=0$ and the exact initial deflection as a function of mode numbers contributing to the ...
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How does a motor produce two different sounds when rotating at two different speeds?
How are two different rotational speeds from the same motor associated with two different sound frequencies produced, i.e., the higher the speed the higher the frequency? Why?
All parts of the same ...
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Tuning fork shape
Hope all is well!
Is it absolutely necessary for a tuning fork to have that well know "U" geometric shape? How important is the geometric shape?
Also, does the mass of that tuning fork play ...
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Material that lets light through only when slightly deformed/vibrating?
I'm curious if there is a material that is porous to light, but only when it is slightly deformed / vibrating. Do such materials exist? In particular I want to prevent a (cheap) laser's light from ...
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How can we find right resonant frequency of a structure?
Structures have infinite DOFs, so it possess infinite mode shapes. How can we find out the right resonant frequency out of the infinite resonant frequencies so that we can save our structure?
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Can natural frequency be produced by damped vibrations?
In my book it's written that when the tuning fork A is is struck on a rubber pad then it starts vibrating with natural frequency (though not written but if it's not vibrating with natural frequency ...
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How does time period of vibration of a body depends on the shape and size of a body?
My books mentions that time period of vibration of a body depends on the shape and size of a body. But it does not give any reason behind the fact. So I searched on the internet but failed to find any ...
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What exactly is the natural frequency of an object?
My book defines natural vibrations as:
THE PERIODIC VIBRATIONS OF A BODY IN THE ABSENCE OF ANY EXTERNAL FORCE ON IT, ARE CALLED NATURAL VIBRATIONS.THE TIME PERIOD IS CALLED ITS NATURAL PERIOD AND THE ...
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How to calculate mode shapes for 2D membranes?
I have a rectangular membrane which is fixed at the edges and undergoes vibrations. I measure the signals (in time domain, so time vs voltage) travelling through this material, through which I can ...
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How long does a large impulse take to travel through a solid?
If I had a 1000km long steel rod and I pushed one end of it, when would someone standing at the other end observe movement? Would it travel exactly the speed of sound in that material, or is the speed ...
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What kind of motion will a string behave when the condition to form stationary waves is not met?
We know that stationary waves can only form when the wavelength of the wave and the length of the string satisfies certain conditions.
My question is, how will the string behave when this condition is ...
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Can we hear sound in a vacuum, if we stand near a black hole?
So we can't hear sound in a vacuum because there's no air to propagate the vibration. But from what I understand, black holes make vibrations in space-time. So much so that scientists can detect black ...
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Plucked string eigenvalues/harmonic frequencies: integer multiples (or not)
I'm trying to derive a model of a plucked string from Newton's second law. My derivation results in $$ω_n = C\cdot\sqrt{n},\, n=1,2,3\dots\text{integer}$$ I think it should be $$ω_n = C\cdot n,\, n=1,...
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Can two standing waves combine to form a traveling wave?
Two traveling waves with equal and opposite wave-vectors form a standing wave, which is easy to prove.
But what about combining two standing waves?
Can we derive the velocity of the wave/disturbance ...
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The resultant amplitude of $n$ equal oscillators
There is a summation related to adding effect of many equal equally spaced oscillators.
I was reading the first few lines of Feynman's lectures on physics (chapter 30) and the way Feynman did the ...
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How to determine the forced frequency response using Fourier transform?
I would like to determine the forced frequency response of the following vibrating system using the Fourier transform method:
$$m\ddot{x} + c\dot{x} + k = f_0\sin(\omega t) \tag{1}$$
So by obtaining ...
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Sound proofing: mass-spring-mass or mass-mass-spring?
I am trying to improve the sound proofing of a metal box. The box is made of steel of thickness $0.8 \;\mathrm{mm}$. I have additional sheets of steel with $3 \;\mathrm{mm}$ thickness for ...
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Is there any way to obtain the velocity of the wave from the Chladni plate pattern?
Chladni pattern is generated because of the vibration of the membrane. One can produce the vibration from acoustic source or directly vibrating the plate. When I looked at the (equation 1) that is ...
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How do standing waves produce a note?
I just learned standing waves in class. And I know that fundamental frequency is the minimum frequency with which a standing can exist on a string. Then we talked about the role of standing wave in ...
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LO vs. TO phonons in a quasi-2D polar crystal at $Gamma$ point
In a polar quasi-2D crystal like hexagonal boron nitride, there seems to be a finite energy/frequency difference between the in-plane LO and TO phonon modes at the center of the Brillion zone (the $\...
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Does damping cause a gradual change in frequency? [duplicate]
Consider a vibrating cantilever in a system where air resistance is taken into account. The air causes the damping of the cantilever's oscillation. As a result, does the frequency of the vibration ...
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Notation for molecular vibrational levels and population inversion
How do I interpret the notations (e.g. (0 0$^0$ 1)) for molecular vibrational levels like in the following diagram for CO$_2$? Also, since one can excite multiple quanta of the same vibrational mode, ...
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Normal Mode in a Vibration?
What exactly is the Normal Mode? According to me, it forms a basis functions (where Max transverse amplitude is fixed wrt position), and all arbitrary vibration in the string can be written in the ...
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What frequency ratio causes maximum transmissibility?
I am doing a problem that asks me to design a vibrational isolator with a moving base providing the excitation. I am given the mass and stiffness, and my solution is constrained by $X/Y < 1.8$ when ...
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How fast can molecular vibrations become under the application of IR radiation?
It is my understanding that IR radiation can be absorbed by molecules when the frequency of the photon matches the natural frequency of the bonds in the molecule which can cause the amplitude and ...
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What is the meaning of the eigenvalues in a damped system?
I am studying the eigenvalues of a an $n\times n$ damped system, such that I get a quadratic eigenvalue problem in the following form:
$$\text{det}(\lambda^2\mathbf M + \lambda\mathbf C + \mathbf K)=\...
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Period of a stationary wave VS Period of vibration of a stationary wave
Is there any difference between these terms? I tried to find on Google, but couldn't. In a question I was attempting, it stated the period of vibration of stationary wave and in the answer, it implied ...
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Does a single atom vibrate?
Thermal vibration looks impossible, but does a single atom in vacuum vibrate due to the electrons' or subatomic particles' actions? If yes, how much is that vibration and is there a way to stop it?
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Does resonance frequency along with variation in length and mode of vibration make it invariant?
I have been doing a question based on a resonance column tube in which tunning fork of $800 \ \text{Hz}$ is used. The water level is changed, so as to attain different lengths which in turn also ...
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The Harmonic approximation for lattice vibrations in Ashcroft and Mermin?
Edit and TLDR:
For classical lattice vibrations, Ashcroft and mermin (pg 424) determine that the harmonic term in the potential energy expansion is
$$
U^{harm}=\frac{1}{4}\sum_{R\, R', \mu \,v}[u_{\mu}...
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Boundary condition on a finite vibrating string with forced vibration
Context
Considering a finite string of length $L$. We suppose gravitation is negligible. The string is only moving transversaly, in $y$ direction, with small amplitude. The tension of a string is $T$.
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Balance equation for a string-spring system: meaning of 2nd Newton's law for massless objects $m=0$ [closed]
The usual homogeneous one dimensional wave equation for transverse (vertical) vibrations is given by
$$u_{tt}-a^2u_{xx}=0,\qquad a=\sqrt{T/\rho}$$
where $u=u(x,t)$ is the vertical displacement, $T$ is ...
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Why does the garden hose swing back and forth? Is my explanation right?
The image is taken from this video.
We notice that the hose in this video is always curved and never straightened. It gives us the feeling that there is always a force perpendicular to the outlet ...
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