# Vibrations Definition and 30 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. ### 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...
2. ### 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.
3. ### 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...
4. ### 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...
5. ### 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...
6. ### 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...
7. ### 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...
8. ### 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...
9. 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...
10. ### 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...
11. ### 2 DOF Vibrations 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...
12. ### 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...
13. ### 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...
14. ### 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...
15. ### 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...
16. ### 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
17. ### 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...
18. ### Normal Modes and Normal Frequencies

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...
19. ### A Why are vibrations so common?

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?
20. ### Why Time Response Characteristics Derived from Zero State Equation

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...
21. ### Good source homework problems for beam spring structures?

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...
22. ### Why is Sound produced

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...
23. ### Medical Why do we enjoy listening to music?

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...
24. ### Longitudinal Wave Equation from Transverse One

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...
25. ### Spring mass pulley system frequency equation

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...
26. ### Equation of Motion for pendulum suspended from a spring

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...
27. ### Vibrations in a solution

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...
28. ### Vibrations of a circular membrane with free ends

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...
29. ### Vibration/Centrifugal Force Question

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...
30. ### M.S. Mechanical Engineering in Mechanics vs Robotics/Controls

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...