What is Vibrations: Definition and 235 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. giodude

    Mass hanging on a steel wire

    Hi, I solved part (a) and will provide my solution below. However, I've been working on part (b) for quite a bit and reviewed the provided, relevant text a few times now but haven't been able to find what I'm missing: Solution (a): Using ##A = \frac{\pi \times d^{2}}{4}##, ##k =...
  2. T

    Where Can I Find Real-World Examples for Mechanical Vibration Problems?

    Good Morning These documents suggest a good text on Vibrations. https://www.academia.edu/34400682/Mechanical_Vibrations_4600_431_Example_Problems?email_work_card=reading-history If you read the PDF, you see MANY example problems. However, each and every one is an abstract schematic. I keep...
  3. K

    A Vibrations in a bow-tie cavity

    Hello! I am trying to build a bow tie cavity and it seems like I am dealing with a large amount of vibrations (I think!). When I scan the laser frequency over one cavity FSR (the cavity is not locked to anything), I see just one peak, which I think it means that I am at least mode matched...
  4. G

    Engineering Vibrations of a rod and vertical spring with 60 degree angle offset

    This is the problem I am working on at the moment. The question states that the bar is at rest in this state. At a 60 degree angle to the horizontal and supported by the vertical spring at B. Small oscillations are introduced and I am required to find the equation of motion and the natural...
  5. M

    A Vibrations in building a cavity

    Hello! I am trying to build an optical cavity and I am having some issues with vibrations. I attached below a plot of the acceleration in x, y and z as a function of time, when the accelerometer is placed on the optical plate (x is red, y is green and z is blue; I shifted them upwards for...
  6. B

    A Measuring new forces with molecular vibrations

    Hello! I noticed in several papers describing high resolution vibrational measurements in diatomic molecules, such as this one, in the conclusion section, that they mention that we can search for new forces (or deviation from gravity inverse square law) between the 2 nuclei by measuring well...
  7. T

    Vibrations, Modal Analysis and Mechanical Systems

    Hello I have used and enjoyed the textbook: "Theory of Vibrations with Applications," by William Thomson However, many of the examples there are more civil engineering than mechanical. There are many good examples of "buildings" under vibrations (good examples, but civil, nonetheless) The few...
  8. M

    I Vibrations of waves with pinned vs free boundary conditions

    Hi PF! Can someone explain to me why in math/physics the frequencies associated with waves (or say drum heads) tend to be larger when the boundaries are pinned as opposed to free? If possible, do you know any published literature on this? Thanks!
  9. B

    Classical Opinions about these textbooks for vibrations and waves

    Hi. I am going to enter uni this October as a first year physics major.One of the first courses I will take is Vibrations and Waves,and the recommended materials are as below: French,Vibrations and Waves Pain,The Physics of Vibrations and Waves, 6th Edition According to Amazon's review,there...
  10. N

    Silence of Canadian Cities: COVID19 Lockdown and Seismic Vibrations

    On 11 March 2020, the World Health Organization (WHO) declared Coronavirus disease (COVID-19) as a pandemic. By then it had spread to at least 110 countries. The announcement made by WHO had a cascading effect. Cities, territories, and countries around the world ended up declaring states of...
  11. Diku Khanikar

    Waves and vibrations on a string

    Q.1. The length of a stretched string fixed at both ends has a length of l=10 cm, mass per unit length ρ= 0.01 gm/cm. If the tension ' T ' is produced by hanging a 11 kg weight at both ends of the string, then calculate, a) The wavelength of the first two harmonics, b) The speed of the wave...
  12. aligator11

    Engineering Homework problem - Pendulum oscillatory system

    Hi All, Anyone willing to help out in explaining what eigenfreuqncy for this oscilatory system, would be? Also if anybody knows the equation to calulate this stuff please, if you're willing to share I'd be greatful! Thanks, regards.
  13. M

    Engineering Mechanical Vibrations - 2 DOF System - Rod with 2 springs

    Hi, So the question is to: derive the equations of motion for the following in terms of x1 and x2? The bar is assumed to be light and rigid. (NB. I know I posted another vibrations problem earlier in which I tried to use an energy approach to get to the equations of motion. However, we haven't...
  14. currently

    Deriving the first-order system for this governing equation

    I tried finding the solution of the equation itself but it hasn't helped! Links to concepts would be greatly appreciated...thank you...
  15. A

    Find the Total Energy of the String

    Steps that I've taken: First, compute the derivative of the psi-function with respect to time and then take the square of the result Second, input the result into the KE integration formula. All that is left is to find the integrand, however this is where calculations became really "messy". It...
  16. S

    I Strain of of a bubble's surface interface during vibrations

    Imagine a bubble vibrating in air. Because it vibrates, it's interfacial area increases, thus new molecules are added and removed from the surface as it vibrates. Consider a molecule is initially at position X_0 at the interface, and over a certain amount of time molecules squeeze and disappear...
  17. I

    I Molecular Vibrations: Rotational and Translational Movement

    Summary: Do solid particles rotate or transit or they just vibrate? Do solid particles move rotationaly and transitionally or all of these for liquid and gas?
  18. V

    Mechanical vibrations: colliding blocks

    I saw this general formula: ##w_{0} = \sqrt{\frac{k}{m}}## In my case both masses after collision create connected system, so ##w_{0} = \sqrt{\frac{k}{m+M}}## Plugging it into ##\omega = \sqrt{\omega_{0}^2 - \beta^2}## gives : ##\omega = \sqrt{\frac{k}{m+M} - \beta^2} = \sqrt{80 - 21^2} <...
  19. V

    Mechanical vibrations: floating apple

    Can someone double check my calculations? I will skip ##\theta## shift angle in all calculations for simplicity. ##x(t) = Acos(\omega t) \quad \land \quad \omega = \frac{2\pi}{T} \quad \land \quad A = \frac{1}{50}m = h## 1.1: ##x(\frac{1}{4}T)## = ? ##x(\frac{1}{4}T) = Acos(\frac{2\pi}{T}...
  20. V

    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##...
  21. Z

    Vibrations: A momentum impulse starts a mass into oscillatory motion

    The fig. 1.1(a) is a mass m attached to a spring that is fixed to a wall. I don't understand what does "a sudden momentum impulse" means. Is it an external force o what? I imagined that the new equation of motion would be md^2x/dt^2+dp1/dt-kx=0 md^2x/dt^2+mdv1/dt-kx=0 is this the equation i...
  22. N

    How does Quadruple Pendulum isolate LIGO from Seismic Vibrations?

    On 28 November 2018, a lecture was given by Dr. Rainer Weiss (2017 Nobel Prize Winner for Physics) at the Ontario Science Centre, Toronto. The lecture was about his work with the Laser Interferometer Gravitational-Wave Observatory (LIGO). In his lecture talked about quadruple pendulums or...
  23. R

    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...
  24. C

    MHB Vibrations of a Hanging Chain: Modeling Tension with PDEs

    Dear Everyone, I am having trouble with how to start with one part of the question: "In this exercise, we derived the PDE that models the vibrations of a hanging chain of length $L$. For convenience, the x-axis placed vertically with the positive direction pointing upward, and the fixed end...
  25. R

    The problem of excitation of vibrations during collisions

    Homework Statement Dear colleagues, my problem is following: The ball of mass with the initial velocity collides with a system of two identical balls of mass each, connected by a massless hookean spring with stiffness and length . It is necessary to find the final velocities of the...
  26. F

    How to calculate vibrations on a rotating shaft?

    Is there a way to calculate the vibrations on a shaft rotating at a certain rpm? Is there a way to accurately simulate this?
  27. A

    Eigenfrequencies of a multiple DOF system

    I am confused with this concept. So if a system possesses multiple possible eigenfrequencies (and therefore modes), how does the system "know" which eigenfrequency will it want to vibrate on? Does that depend on the initial condition you give the system? Is there any mathematical relation...
  28. M

    Car test, and vibrations problem

    Homework Statement in tests to choose the most comfortable shock absorbents, 3 cars are used, with the same mass "m", and the same springs, but different shock absorbents. the graphs show the changes in car height when passing over a bump (y=0 being the normal state of the car). . . . -Witch...
  29. S

    Elasticity and light speed vibrations

    Special relativity requires any substance to be compressible. Indeed, if an item were made of a perfectly rigid substance, then move one end of it, and the other end must move at the same moment - the movement must be transmitted instantly, faster than light. Thus, the special relativity sets...
  30. tomadevil

    General Question about Vibrations

    Hello Everyone, I conducted an experiment with a metal beam which had a motor attached to it in with an eccentric mass on it. The two ends of the beams were fixed with a roller and a hinge(as I remember). This was a one degree of freedom experiment. I had to collect data during free/forced...
  31. M

    Why do hot metals emit radiation - atom vibrations?

    Why does a tungsten filament light bulb (or any heated metal for that matter) emit EM radiation (both visible and infrared) - is the EM radiation due to vibration of molecules or electron excitation?
  32. Ben Geoffrey

    I Free Vibrations of a linear triatomic molecule

    This question is regarding equation 6.59 in Classical Mechanics Goldstein 3rd edition. I don't understand how he reaches that step. He says he does by inverting 6.41. Is he taking the transpose matrix composed of the eigen vectors by meaning inversion ? I thought I could upload the screenshot...
  33. thepikminman

    Vibrations - Modeling system, equation of motion

    Vibrations - Modelling system, equation of motion Hi, In the first question (question 4) in the attached file, how would you go about modelling the system and finding the equation of motion? All those masses are confusing me, I don't even know where to start. I don't know whether the angle...
  34. B

    Waves and Vibrations -- Vector Diagram

    Homework Statement A lightly damped oscillator (mass, m, and spring constant,s, damping constant, b, with one end fixed) under external harmonic force (F0cosωt).(i.e., Standard mass-spring system with lubricated damper, and driven by an external harmonic force.) Since it is lightly...
  35. S

    I Vibrations of astronomical bodies

    Pulsars are known to rotate at very predictable frequencies. If a beep or short tone is assigned to each rotation, the spin of the star can be 'sonified'. Pulsars spin anywhere from a few fractions of times per second to over 600 per second. 600 cycles is audible in the human range of hearing...
  36. MathematicalPhysicist

    Effect of Lattice Vibrations on Vacancy Formation.

    Homework Statement I am not sure I understand how did they solve question (b). Here's the solution to question (b): Homework EquationsThe Attempt at a Solution For the first approximation I plugged everything to the identity in (a) and indeed got the approximation as it's written in the...
  37. H

    Understanding Resonance in Underdamped Forced Vibrations

    What is the condition for resonance to occur in case of underdamped forced vibrations?
  38. JTC

    I Meaning of the word "Harmonic" in different contexts

    A harmonic function is one that satisfies Laplace's equation -- a definition cannot be more precise than that. However, in the study of vibrations, sine and cosine are considered harmonic functions; but they don't solve Laplace's equation. And then there are words like: harmonics (for higher...
  39. Feodalherren

    Vibrations in cantilever beams

    Hi fellow mechanical engineers, I am designing a rather simple excel program for work that deals with vibrations in robots. Imagine a robot that is made up of linear axes that can move in x,y,z sort of like a 3D printer, take a look at this picture: https://pasteboard.co/8hvV5vf.png Focusing...
  40. K

    Can I Use a Non-Symmetrical Matrix in Simulink for My 2 DOF Vibration System?

    Homework Statement I have the following system, I believe I've correctly established the equations. I'm having trouble building a working schematic bloc in Simulink. Homework Equations The Attempt at a Solution In the following equations Ktrain = Ka and Ctrain = Ca I know my matrix should...
  41. W

    Can somone explain this review solution (vibrations)?

    Homework Statement Homework Equations The equations are all given The Attempt at a Solution This isn't really a homework question... it's solved, but I'm having a hard time following it. I don't understand where the first term: -a(kaθ) comes from. I can see it's the moment relation...
  42. Kaneki123

    B A question about Vibrations....

    Okay...I just have a simple question...For a vibrating pendulum, a one complete cycle is considered when it displaces from a certain position A and then again returns to that certain position A...My question is that the damping is continuosly taking place on the pendulum, so there is no way that...
  43. ramzerimar

    Mechanical vibrations + Aerodynamics?

    I'm now taking classes on mechanical vibrations and fluid dynamics, and those are two fields that are very interesting to me. I've always liked the subject of aerodynamics, but now I'm really liking to study mechanical vibrations, very interesting field of study. I'm looking for some specialty...
  44. ReidMerrill

    IR active vibrations and point groups

    Homework Statement In lab we synthesised cis and trans copper glycine and we have to use IR to differentiate the two so we have to figure out the number of IR active vibrations for each complex. It's been a year since I did anything with point groups so I'm not sure if I did it right. Homework...
  45. sistruguru

    I How far do vibrations from a vehicle emanate?Doppler effect?

    So I have a strange question. I study snakes, which are of course sensitive to vibrations in the ground. A common technique for finding snakes is to drive roads at night. A constant debate that comes up among herpetologists is whether or not the vibrations of the vehicle are causing the snakes...
  46. T

    Sound of vibrating string - modes

    Homework Statement Suppose we listen to the sound of a vibrating string with a pickup that is sensitive to the motion at a point 1/3 of the string's length from one end. Which statement is true? A.) We will be able to hear all of the modes except the third B.) We will not be able to hear the...
  47. M

    B The Sense of Restoring Force in Vibrations

    I would like to ask about the sense of the restoring force in mechanical vibrations. Comment 2 says that resultant force is opposite the motion but I have some hesitations about it because let's think the situation that mass is moving back upward to its equilibrium position. In this case the...
  48. A

    I with the free vibration of bar problem

    Homework Statement Find the free vibration of the bar supported by a spring and a viscous damper (See attached figure) Homework Equations (a)Derive the equation of motion (b) Obtain the moment of inertia of bar (c) obtain natural frequency when d=0. The Attempt at a Solution
  49. W

    Natural frequency of a mass spring system

    Homework Statement Homework Equations T = 2π√(m/k) mx'' + kx = 0 F = ma The Attempt at a Solution I don't honestly know where to start with this. I'm really out of my league in this class, and I'm trying my best to catch up with the things I didn't quite master in Dynamics and Physics... As...