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.
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 =...
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...
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...
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...
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...
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...
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...
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!
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...
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...
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...
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.
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...
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...
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...
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?
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} <...
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##...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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?
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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
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...