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.
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.
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...
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...
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).
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-Witch...
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...
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...
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...
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...
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...
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...
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...
Homework Statement
I have to determine the frequencies of the normal modes of oscillation for the system I've uploaded.
Homework Equations
[/B]
I determined the following differential equations for the coupled system:
\ddot{x_A}+2(\omega_0^2+\tilde{\omega_0}^2)x_A-\omega_0^2x_B = 0...
Vibrations are everywhere and the question is if there is some fundamental reason for this. Per example, symmetries and the least action principle are behind the conservation laws. What is the reason that vibrations are so common?
QUESTION:
1) Why are Time Response Characteristic's Expressions derived from only from Zero State Equations?
NOTE: Nise Control Systems Engineering 6ed uses step inputs to derive Time Response Characteristics for 1st
and 2nd order ordinary differential equations...
Hello there,
In this semester I'm studying the vibrations course. In this course we get questions like calculating the total stiffness, set up differential equations and so on. The book that we use (Theory of Vibrations) has not been very useful, our exams give beam spring structures related...
Why is sound produced?
Say, for example, when a stone hits a tin box a sound is produced. Why is this sound produced?
Even if the sound is produced in the ear, we generally say that the vibrations of the ear drum produces the sound, why is it produced. Why does vibrations produce sound.
Even a...
I've been researching this subject for a little while. I'd like to hear your ideas, because the topic is widely discussed.
So here is some part of my research which makes my opinion quite clear:
"Sometimes we say , that one is moved by music. Of course, it does not mean for him/her to be...
Homework Statement
Please see attached.
Part ii)
Homework Equations
The Attempt at a Solution
So I try to conserve volume as it suggests in the hint. I take the initial volume of the region to be given by:
$$ h \times \delta x \times l = (\delta x + \eta) (h+\Psi) l $$
Where l is just some...
Homework Statement
A spring is attached to the ceiling, a pulley is attached to the other end of the spring, a string is suspended over the pulley, and a mass attached to the free end of this string. The system oscillates vertically.
Can someone PLEASE help me derive this equation for natural...
Homework Statement
Derive Newton's and Lagrange's equation of motion for the system. Discuss differences and show how Newton's equations can be reduced to lagrange's equations. Assume arbitrarily large θ.
The system is a pendulum consisting of a massless rod of length L with a mass m...
Hi, I was wondering if someone can explain to me the following. If I have a vibrating molecule in a solution, what effect would this vibration have on other particles in my solution which are different. Can the vibration be the same for them if they are not excited (do not vibrate due to...
Hello,
As of this moment I am trying to get in the process of writing an Extended Essay on Chladni Plates, more specifically on a circular vibrating membrane with free ends. To begin with I thought the concept could be simplified to such an extent where I could take a cross-section of the plate...
Hello
I am making a vibration project which requires me to mount eccentric weights on both sides of an electric motor. I must submit the "generated force(in Kg)" by this motor.
The RPM of motor = 1000
Total weight on both sides of the motor = 16.8Kg (8.4Kg on both sides)
The radius(distance...
Hello fellow PF members,
I'm currently in my senior year in Mechanical Engineering at Oregon State University. I'm considering going on to get my Master's Degree to gain more knowledge (since I'm fascinating by them). I really like Math and have a Math Minor already. I am looking to go into a...