# What is Vibration: Definition and 473 Discussions

Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin vibrationem ("shaking, brandishing"). The oscillations may be periodic, such as the motion of a pendulum—or random, such as the movement of a tire on a gravel road.
Vibration can be desirable: for example, the motion of a tuning fork, the reed in a woodwind instrument or harmonica, a mobile phone, or the cone of a loudspeaker.
In many cases, however, vibration is undesirable, wasting energy and creating unwanted sound. For example, the vibrational motions of engines, electric motors, or any mechanical device in operation are typically unwanted. Such vibrations could be caused by imbalances in the rotating parts, uneven friction, or the meshing of gear teeth. Careful designs usually minimize unwanted vibrations.
The studies of sound and vibration are closely related. Sound, or pressure waves, are generated by vibrating structures (e.g. vocal cords); these pressure waves can also induce the vibration of structures (e.g. ear drum). Hence, attempts to reduce noise are often related to issues of vibration.

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1. ### Tuned mass damper does not reduce the amplitude of vibration?

Hello everyone, I have a simple question. Lets say a single degree of freedom system (SDOF) which consists of a spring and a mass is excited by an external force. The SDOF system has the eigenfrequency of 0.31 Hz and the external force is a periodic force with the frequency of 0.6 Hz. After...
2. ### I Could vibration carry electricity or something else?

A vibration moves along until it has moved too far or there is no other objects to travel to, so does that mean it could carry electricity or something chemistry related?
3. ### Random Vibration Fatigue Analysis

Hi Everyone, I'm trying to do a "Random Vibration Fatigue Analysis" on a bracket assembly that is mounted on the headboard of a pickup truck. BACKGROUND: The bracket assembly is mounted on the headboard of the truck using 2xbolts (1 per each mount). The truck regularly travels on a rough...
4. ### B How Fast Do Different Atoms Vibrate?

The "ticks" of the current standard atomic clocks are marked by the regular vibrations of an ensemble of cesium atoms, which vibrate 9.2 billion times every second How about other atoms, how fast does these vibrate ? And where is possible to ready about this ?
5. ### B Vibration Patterns of Strings within Quarks?

Is it possible to study/observe the virbation patterns of a string within a quark? I understang that String Theory is a theoretical framework, however is it possible to make an observation linking the vibrations of the strings within the quarks to the particles produced? If so, has there even...
6. ### Free vibration in 2DOF spring mass systems

I am completely new to this subject and I am trying to find out how I read data off a displacement vs time graph to find the natural frequencies and mode shapes. Lecturer hasn't provided any materials on graphs, just looking for some help and where to go so I can understand it. Thank you
7. ### Vibration and Modal Analysis: Adding massless springs to a shaft

Hello, I am working on vibrations and modal analysis recently. I have a question that I could not find any answer. Can you please help me? Imagine a shaft. When we run the free free modal analysis lets assume that first bending mode is 600 Hz. Then we add 2 massless springs to the shaft. The...
8. ### I Where do the vibrational modes of molecules come from?

Hello everyone. First, sorry for my english. Second, I have got question where vibration mode of H2+ molecule (I think it is the most simple molecule for this topic explanation) comes from. If I should get basics before asking this tell me :). By my count the most important factor behind "being"...
9. ### Engineering Calculating Footfall Induced Vibration: Troubleshooting and Tips

Hey guys. Im about to learn about footfall induced vibration. However i want to reach the same results as in the pdf page 44 ''design guide for footfall analysis'' i get 0.000726 while they get 5,79E-0,4. Can anyone help me figure out what im going wrong and where i have made a mistake?
10. ### Understanding Molecular Vibration of HF: Equilibrium Distance and Binding Energy

Starting with a), I have learnt that the potential energy function has a minimum at the equilibrium distance ##a##. So at the equilibrium distance the derivative of the potential energy function should equal zero: ##\begin{align} V'(a)&=-\frac{4A}{a^5}+\frac{B}{a^2}=0 \nonumber \\ \iff...
11. ### I Planck’s constant: Why are atom vibration frequencies integers only?

Given the definition of whole numbers as integers, https://www.google.com/search?q=what+is+a+whole+number&rlz=1C1VDKB_en-GB&oq=what+is+a+whole+number&aqs=chrome..69i57j0i512l9.11619j0j15&sourceid=chrome&ie=UTF-8 Is it known why atom vibrations are only at whole numbers ( ref plank’s constant)...
12. ### Study of harmonic motion of a liquid in a V shaped tube

A V-shaped tube with a cross-section A contains a perfect liquid with mass density and length L plus and the angles between the horizontal plane and the tube arms as shown in the attached figure. We displace the liquid from its equilibrium position with a distance and without any initial...
13. ### Engineering What kinds of jobs can a vibration engineer with this experience?

Hello guys, I've been searching job to my father. Because the economical situation of the country he wants to find a foreign job. -He has 20+ years working as an director of vibration analysis and diagnosis company who himself founded. -He has 20+ years working as mechanical engineer teacher...
14. ### How to get the transfer function for force transmissibility of a wall?

Hi, I am trying to get the transfer function from a wall between rooms. From one side I have the force of a hammer as an input ,and in the other side of the wall (next room) I have an accelerometer. Is it possible to get the TF without know the damping, stiffness and mass of the wall partition...
15. ### How to express ωₙ in terms of only mass (m) and stiffness (k)?

Summary: How to express ωₙ in terms of only mass (m) and stiffness (k)? I tried doing it with F=kx but it is out of my ability to simplify it to only m and k. Here is my approach:
16. ### Vibration: Transmissibility ratio sign change when damping is equal to zero

So for the transmissibility ratio equation, after doing a lot of questions when damping is zero and I have to take the square root of the denominator. Some questions take the positive root (1-r^2) while for other questions the solution takes the negative root (r^2-1). Can someone explain when we...
17. ### I hate my vibration class (vent)

I legit absolutely despise this class. I did all the homework but still did trash on both the first 2 term test. There’s 1 million equations and I don’t even know what graph represents what. Professor doesn’t do any examples and gives homework problem that barely help. I don’t even want to...
18. ### I Conservation of finite difference for vibration equations

Let's discuss whether the energy under a finite difference (FD) scheme is conserved. Take the simplest vibration eq mx''+kx=0, which one will use a FD scheme to solve. The energy is mx'^2/2+kx^2/2. Whether the energy is conserved doesn't depend on the FD scheme for the ODE but upon the FD scheme...
19. ### Equations of motion of a 2-DoF Free damped vibration system

Summary:: What are the Equations of motion for a free damped 2-Dof systrem? Hello, I am required to calculate the equations of motion for a 2-dof system as shown in the attached file. The system is undergoing free damped vibrations. I have found the equations of motion for no damping but i...
20. ### A Calculating noise of a transducer from molecular vibration

I'd like approximate the noise floor of an ultrasonic air transducer starting from molecular vibrations. Simply put, if I treat atmospheric air as an ideal gas and I confine each air molecule to exist in a volumetric cube with a square face ##A_\mathrm{face}##, then I approximate the number of...
21. ### A Is there a vibration energy term associated with mesons?

Hello, I am learning about solutions of the Schrodinger equation including the term of rotational energy (i.e. L^2 /2I, in its quantized form) and I was wondering if there should be another quantum term describing vibrational states of hadrons or any other composite subatomic particle, in...
22. ### Harmonic forced vibration of a cantilever beam

Hi, in the book titled "Formulas for Dynamics, Acoustics and Vibrations" by R.D. Blevins, I've found a formula that can be used to calculate the bending stress in a cantilever beam subjected to harmonic force applied at the free end. The formula looks like this: \sigma=\frac{F_{0}Ec}{m...

24. ### I Normal modes of vibration from the total energy

A mass ##m## is restricted to move in the parabola ##y=ax^2##, with ##a>0##. Another mass ##M## is hanging from this first mass using a spring with constant ##k## and natural lenghth ##l_0##. The spring is restricted to be in vertical position always. The coordinates for the system are ##x##...
25. ### Effect of initial stress on the natural frequency of vibration

Hello all, We might have observed that by tightening a string of a musical instrument, the natural frequency of the string changes. But I can not describe this phenomenon by the theory of linear elasticity. Also if we simulate the vibration of a bar with the help of structural software tools...
26. ### I How Is the Solution to the Vibration Equation Derived?

Hello,everyone: I got an equation: \ddot{x} + \omega_{0}^2 x = {e \over m} E_{x} I know the solution is: x(t) = {e \over {\omega_{0} m}} \int_{0}^{t} E_{x}(\xi) \sin{ \omega_{0} } (t - \xi) d \xi \\ x(0) = \dot{x} (0) = 0 My attempt to...
27. ### I Vibration Problems -- Why must there be two solutions to the DE?

Consider the second order linear differential equation that describes vibration: Mass, damping, stifffness and free vibration If the roots of the characteristic equation are repeated, we have one solution and we must search for a second. We assume it by taking the first solution and...
28. ### I Justify Assumption of Exponential Response to Free Vibration Problem

Consider a free vibration problem of a mass in 1D: inertia, damping, spring, and no forcing function. We begin by assuming an exponential response. And then run through all the cases of under, over, critical damping, etc. I am fully aware of Euler's formula that relates sine/cosine to complex...
29. ### Influence of initial shift on undamped frictionless forced oscillations

I have general equation for undamped forced oscillations (no friction) which is: I just wonder about,what type of motion should occur when initial conditions are both 0 (i.e v0=0 and x0=0). My intuitive expectation is that as there is no 'natural' oscillations at beginning,vibration has to be...
30. ### The meaning of eignvalues in vibration

when i solved simple example about 2 height stories when we have 2 degree of freedom I’m confusing about the meaning of result of eigenvectors and eigenvalues . This is the example i'm getting 4 eigenvalues and 4 eigen vectors . as following I didn’t understand we have 2 MDOF and we are...
31. ### Infinite-Extent 2D Mass-Spring System vibration and dispersion relation

Hi, I am trying to find equation of motion and its solutions for a 2D infinite lumped mass spring system as depicted in figure. All the masses are identical, All the springs are identical, and even the horizontal and vertical periodicity is the same n=a. I need to try find dispersive relation...
32. ### Does Increasing Mass Affect the Natural Frequency of Vibration?

My query here is, Suppose there is a 2 kg mass To oscillate it/vibrate it, it will take some force and it will have some natural frequency Now I increase the mass to 5 kg so to vibrate it, won't it take more force and so at the end, won't the natural frequency of the object increase? as its more...
33. ### Micromechanical Vibration Analysis of Composite Materials

This project is stressing me out along with other workload and I'm in panic mode right now. The brief of the project is in the attachment. I can interpret 4 objectives out of this: (1) Analysing the relation of the physical parameters in the composite material with the characteristics of wave...
34. ### I Resonance gets sharper just by increasing the resonance freq, why?

The ##Q## factor of an oscillating system is defined as ##\omega_{r}/\Delta \omega##, where ##\omega_{r}## is the resonant frequency, and ##\Delta \omega## the resonance width. As I understand, ##Q## measures how sharp the resonance curve is. Why is it that the resonance curve gets...

36. ### I Question about the Derivation of the Equations of Vibration

For undamped free vibrations, we have the following differential equation. mu'' + ku = 0 where m is the mass of the object hanging on the end of a spring, and u is the distance from the equilibrium position as a function of time. This yields u = Acosωt + Bsinωt where ω is √(k/m)...
37. ### Transient vibration of an engine

How is the transient vibration of a piston engine usually simulated? I know that in order to define the vibration loading you need the mass properties and dimensions of the moving components plus the cylinder pressure curve. And of course you need to know the firing order, V-angle (if...
38. ### A Find Reduced Mass for Polyatomic Molecules

Summary: How could we find the reduced mass for polyatomic molecule ? I have problem with reduced mass of poly atomic moleculs because for diatomic molecules you can easily find out the reduced mass by M¹M²/M¹+M²,but I don't think with this way we can find reduces mass for example for fe²o³?
39. ### Dynamics of Machines - Forced Vibration

Summary: I need a help to solve problem asked in university exam I am looking for the answer for the above question. I solved almost except the last one "Force exerted by the spring and dashpot on the motor". Can anyone help me to find out the answer for it
40. ### Noisy Chiller: Solutions to Reduce Vibrations

Dear forum members, We have a water cooled chiller device (see its model in attached link) and we use it to cool a hot mirror element. Unfortunately the chiller is vibrating and the vibrations couple all the way to the mirror through a pair of rubber tubes (1cm in diameter, 2m in length) and a...
41. ### Turbo pump - vibration and noise at a certain RPM

I have picked up a used pfeiffer turbomolecular pump and controller for pretty cheap. It runs like a champ, completely smooth and quiet except for when it’s first starting up. As it approaches 5500 rpm, it starts vibrating somewhat and sometimes produces a momentary scraping noise when the...
42. ### Trying to better understand sound & vibration on textured surfaces

Hi, First thank you in advance for reading and answering my question. I am very much a newbie when it comes to physics, so while I feel my question in pretty straight forward I'm sure it's more complex than my thinking. OK so here it is... Does the texture of two surfaces change the decibel...
43. ### Mechanical vibrations: maximum velocity

So I am almost sure I know how to solve this, just curious about the maximum velocity. Anyway, if you could double check my calculations, here it is. ##T = \frac{t}{n} = \frac{10s}{15} = \frac{2}{3}s## ##\omega = \frac{2\pi}{T} = 2\pi \frac{3}{2} = 3\pi## a). position at ##t = 0.8s##...
44. ### I Which is Better for Measuring Vibrational Systems: Free or Forced Vibration?

Problem Statement: How to measure the natural frequency and damping ratio of a vibration system? Why are the advantages over one another? Relevant Equations: natural frequency, damping ratio of a vibration system I think there are two ways: free & forced vibration. forced is used because it...
45. ### I Is a photon simply a vibration of the spacetime lattice?

Is a photon simply a propagating vibration of the spacetime lattice similar to gravitational waves but at a different wavelength and amplitude, and the electron that creates it plucks a single lattice string rather than a bunch? Therefore it has no mass and travels differently through spacetime...
46. ### Find suitable SI units to work with a Vibration Sensor

We are working on an IOT project in which we are trying to learn about different vibrations of using Wireless Vibration Sensor According to the manual, the wireless vibration sensor is giving the output while testing on CNC machine device 0.75, 0.71,0.69 whose SI units are in 'g'(which is...
47. ### Vibration testing on shaker - High amplitude observed

Hello everyone, I wanted to gather opinion from anyone experienced in vibration regarding one of test fixtures I have created for small satellites. The image below shows the Test-POD that I am testing on a single axis shaker. In one of the tests, I had troubles that the amplitude got higher than...
48. ### Standing Wave Fundamental Frequency and Particle Vibration

For a wave A sin ( kx - ωt) and a wave A sin ( kx + ωt) traveling opposite to each other, on evaluating by applying superposition principle , the resultant displacement function is 2A sin ( kx ) cos (ωt) . For different Node Anti-node configurations we calculate natural frequencies of the...
49. ### Frequency of Undamped Driven Oscillator near Zero

Description of the Problem: Consider a spring-mass system with spring constant ##k## and mass ##m##. Suppose I apply a force ##F_0 \cos(\omega t)## on the mass, but the frequency ##\omega## is very small, so small that it takes the system, say, a million years to reach a maximum and to go to 0...
50. ### Find the resistive constant in a critically damped system

Homework Statement This problem is taken from Problem 2.3, Introduction to Vibration and Waves, by H.J. Pain and P. Rankin: A critically mechanical system consisting of a pan hanging from a spring with a damping. What is the value of damping force r if a mass extends the spring by 10cm without...