Damping Definition and 308 Threads

Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples include viscous drag (a liquid's viscosity can hinder an oscillatory system, causing it to slow down) in mechanical systems, resistance in electronic oscillators, and absorption and scattering of light in optical oscillators. Damping not based on energy loss can be important in other oscillating systems such as those that occur in biological systems and bikes (ex. Suspension (mechanics)). Not to be confused with friction, which is a dissipative force acting on a system. Friction can cause or be a factor of damping.
The damping ratio is a dimensionless measure describing how oscillations in a system decay after a disturbance. Many systems exhibit oscillatory behavior when they are disturbed from their position of static equilibrium. A mass suspended from a spring, for example, might, if pulled and released, bounce up and down. On each bounce, the system tends to return to its equilibrium position, but overshoots it. Sometimes losses (e.g. frictional) damp the system and can cause the oscillations to gradually decay in amplitude towards zero or attenuate. The damping ratio is a measure describing how rapidly the oscillations decay from one bounce to the next.
The damping ratio is a system parameter, denoted by ζ (zeta), that can vary from undamped (ζ = 0), underdamped (ζ < 1) through critically damped (ζ = 1) to overdamped (ζ > 1).
The behaviour of oscillating systems is often of interest in a diverse range of disciplines that include control engineering, chemical engineering, mechanical engineering, structural engineering, and electrical engineering. The physical quantity that is oscillating varies greatly, and could be the swaying of a tall building in the wind, or the speed of an electric motor, but a normalised, or non-dimensionalised approach can be convenient in describing common aspects of behavior.

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  1. T

    Determine critical damping of multimass system

    Hi I have a spring mass damper system with multiple masses. Is there any way I can calculate the magnitude of the damping in order to get a critical damped system? I have the scaling of the dampers(c1/c2) and they are connected in series. c_eq=c1+c2... I tried with the formula...
  2. M

    How Does Damping Affect the Behavior of Oscillatory Systems?

    Hello All, I have some basic damping related questions that I am hoping you all can shed some light on or suggest some resources on to someone who has taken a few undergraduate level physics courses. i.) Can someone give me an intuitive explanation as to why linear damping (underdamped...
  3. D

    Simple Harmonic Motion without damping

    So, simple harmonic motion without damping is described generally by x(t) = Acos(\omega*t +\delta) Which is derived from the differential equation x''+\frac{k}{m}x = 0 We know that A = \sqrt{c_1^2+c_2^2} and tan\delta = \frac{c_1}{c_2} With the differential equation, dealing...
  4. Z

    Bump detection using accelerometer inside car, estimating suspension damping

    Homework Statement This is not a homework question, I am working on a project to get it data from how rough the road is, mostly road bumps/pot holes. My project is for a capstone project, I want to use an accelerometer to measure the upward G's on the car frame when goes over bumps, or into...
  5. D

    Phase Lag between Force & Displacement in Forced Vibration w/ Viscosity Damping

    Dear all, Can anyone explain the the phase lag between force and displacement in single degree of freedom forced vibration with viscosity damping? The response of phase angle derived by mechanical vibration as below ( assuming force is excited harmonically) : Phi(ω) = arctan( C*ω / ( K...
  6. Z

    Damping ratio and Maximum overshoot relation

    There is a certain equation relating both Mp (max. overshoot) and damping ration. Which is; Mp = e(-ζ*pi)/(1-ζ2)1/2 What I get from that equation is for every system a certain damping ratio will result the system in a certain amount of max. overshoot. That sounds ridiculous, because...
  7. X

    Vertical Oscillation assuming no damping

    Homework Statement An 85-kg person steps into an experimental car of mass 300 kg, causing it to sink 4.5 cm on its springs. If started into vertical oscillation, and assuming no damping, at what frequency will the car and passenger vibrate on these springs. Homework Equations ω=√k/m...
  8. D

    MHB Explore Attraction Basins of Damped Double-Well Potential Model

    I don't understand how to start. Consider the damped double-well potential model $$ \ddot{x} - x + x^3 + \gamma\dot{x} = 0, $$ where $\gamma$ is the damping coefficient. This model has two fixed points at $(x,\dot{x}) = (1,0)$ and $(-1,0)$. In the phase plane $(x,\dot{x})$, determine the...
  9. M

    Overshoot when solving damping differential equations

    I am trying to solve and plot the differential equations for springs. when the damping factors are under 1 (underdamping), I tried damping ratios of: 0.01, 0.2, 0.1, 0.4, 0.8 If I use the following equations (wd= damped frequency, wn= natural frequency, v0= v initial, x0= x initial, t=...
  10. C

    Natural frequency, damping ratio and steady state amplitude help needed

    (1) A mass of 3.0 kg is suspended from a vertical spring and produces a static deflection of 60 mm. The system is also subjected to viscous damping of 36 N s/m. Calculate the value of the: (a) natural frequency i. In Hz ii. And rad/s (b) damping ratio...
  11. L

    Simple harmonic motion and damping

    I have to solve the following D.E. which describes how the amplitude of oscillation r, changes with time. r=f(t) \frac{dr^{2}cos^{2}t}{dt}=rsint How do I find r?
  12. M

    Gas Strut - Damping coeff and spring constant

    Hello everyone, I'm an engineering student and I have to "size" a gas strut (i.e. spring+damper) to model a trunk lid opening mechanism. I have a problem: on every "datasheet" (something like this http://www.strutsdirect.co.uk/components/variable-force-gas-struts.php) only forces and...
  13. V

    Electron-hole pair damping of vibration, thin film resistivity

    Hello, I'm reading something about adsorbate induced surface resistivity changes in thin metal films and there is often mentioning of electron-hole pair damping, as for example: "electron-hole pair damping of the parallel(to the surface of thin film) frustrated vibration of the...
  14. H

    Help understanding landau damping derivation

    I have been given a derivation describing the physics of landau damping, but i don't quite understand it. It starts with the equation for a charged particle in a 1d electric field varying as Eexp[i(kx-wt)] being determined by d2x/dx2=e/m Eexp[i(wt-kx)]. Since we are dealing with a linearized...
  15. L

    How do you calculate the damping force of a tuned mass damper?

    For a report I am investigating whether a gyroscope could be used to stabilise the skyscraper Taipei 101 instead of the tuned mass damper, I have figured out how to set up the gyroscope but I need to calculate radius, speed of rotation etc. To do this I need to find the equivalent moment exerted...
  16. O

    How to find damping ratio from a graph ?

    I have a graph. I have all its (x,y) values. How can the damping ratio from this graph ?
  17. T

    Determining Damping Constant k From Data

    Homework Statement i had an investigation use your data to find the value of k, compare this theoretical number with your data. - plot a suitable graph so that you can determine k. Homework Equations A= A_0e^(-kn) A_0 initial amplitude = 1 The Attempt at a Solution hey I am new to...
  18. J

    Why does damping affect the time period of SHM oscillators?

    There are two equations that can describe the time period of SHM oscillators (springs / pendulums ONLY) Spring T = 2π * \sqrt \frac {m}{k} Pendulum T = 2π * \sqrt \frac {l}{g} It would seem from these equations that time period is independant of amplitude therefore we should be able to...
  19. E

    Increasing Damping Ratio: Does it Make a Circuit More/Less Damped?

    If the damping ratio of a damped circuit is increased, does the circuit become more or less damped? I would think it would become more damped, but what exactly is the definition of the damping ratio?
  20. Hepth

    Thought Prob : Regenerative Damping of a Simple Harmonic Oscillator

    So I was just thinking about regenerative braking, piezoelectric sensors/strain gauges, magnetic-induced currents etc. and I thought of a question that would make a simple/decent discussion/practice in general engineer/physics (lots of /'s) Suppose you have a simple harmonic oscillator :: WALL...
  21. N

    Door closer spring and damping coefficients.

    I am designing a test rig for golf clubs at the university of nottinghamm, and due to a large spending spree, don't have much of my budget left. As a result of which, I was hoping to use a door closer as a spring damper system. Does anyone have any idea of rough values of the damping...
  22. A

    Damping. Altitude vs. Period which has greater effect?

    Homework Statement This is only part of the problem but this is all I'm having trouble with... Which effect of damping would be more noticeable, the change of period or the decrease of the amplitude? Homework Equations x(t)= Ae^{-\beta t} * cos(w_{1}t - \delta) period = \frac{2Pi}{w_{1}}...
  23. L

    Work done by damping, harmonic oscillator, help?

    Ok here's the question: A body m is attached to a spring with spring constant k. While the body executes oscillations it also experiences a damping force F = -βv where 'v' is time derivative of displacement of the body from its equilibrium position. I believe equation of motion is F =...
  24. J

    Critically Damped Oscillator Spring Constant and Damping Parameter

    Homework Statement A mass of 1000 kg drops from a height of 10.0 m onto a platform of negligible mass. It is desired to design a spring and damper on which to mount the platform so that it will settle to a new equilibrium position 2.00 m below its original position as quickly as possible...
  25. B

    Forced Oscillator where Damping is Negligible

    Homework Statement Damping is negligible for a 0.139 kg mass hanging from a light 7.00 N/m spring. The system is driven by a force oscillating with an amplitude of 1.88 N. At what frequency will the force make the mass vibrate with an amplitude of 0.430 m? There are two possible solutions...
  26. S

    Understanding RLC Damping Coefficient for Non-Standard Circuits

    Hey, Quick question for you guys. How do you find alpha (damping coefficient, Neper frequency) for a circuit that's not strictly parallel or in series? For instance, α for a series RLC circuit is R/2L whereas α for a parallel circuit is 1/2RC; but what if it's different? Homework...
  27. N

    A Damped Oscillator and Negative Damping Force

    A damped oscillator is described by the equation m(x'') + b(x') + kx = 0, where the damping force is given by F = -b(x'). Show that the rate of change of the total energy of the oscillator is equal to the (negative) rate at which the damping force dissipates energy.
  28. L

    Estimating the damping coefficient of a wave assuming a very small ratio

    Homework Statement The original problem is determining the dispersion relation of an ordinary wave in plasma damped by collisions. That part was easy enough but the next part is to find the damping rate (-Im(ω)) of the wave, assuming k is real and \nu << \omega where \nu is the collision...
  29. S

    Dynamic analysis: Effect of damping on frequency

    This is a fundamental question but will be grateful if helped. Please can anyone explain the effect of damping on frequency? Whether, damping increases or decreases the frequency and why? An explanation with a physical interpretation will be gratefully appreciated. Vishal
  30. B

    Damping constant and angular frequency

    While discussing ω^{'}, the angular frequency of a damped harmonic oscillator, given by: ω^{'}=\sqrt{\frac{k}{m}-\frac{b^{2}}{4m^{2}}} where k is the "springiness", m is the mass, and b is the damping constant, my book, Halliday, Resnick and Walker, says if b is small but not...
  31. D

    How Can I Analyze Energy Dissipation in a Non-Linear Damping System?

    Homework Statement vinit = sqrt(2g*h); h = drop distance vfinal = 0; xinit = 0; xfinal = 100mm; a = g; Issue: non-linear damping. M*x'' - b*(x')^2 - k*x = 0; b = 128*mu*(length fluid travels)*(D^4(piston)/[(D(hydraulic)^4)(orifice opening)]every book I've been reading on vibrations damping...
  32. F

    Oscillator with and without damping - Need help please

    An oscillator with natural frequency ω consists of a mass on a spring positioned on a horizontal table. The table is frictionless for x<0 but has friction for x>0 and an effective damping constant K on that side of the table. Find the frequency of this oscillator and the ratio of successive...
  33. J

    RLC Circuit (with critical and heavy damping)

    Homework Statement Consider a RLC circuit. a) Suppose the parameters are chosen to give critical damping. The capacitor is charged to a voltage of V₀ and at time equal to zero the switch is closed. Find the time at which the magnitude of the current reaches a max, and find the value of the...
  34. R

    Free Vibration- Viscous Damping

    Homework Statement Scenario 1: Mass suspended from dasphot (damper) and spring Mass=M Damping Coefficient=c Spring Constant=K Scenario 2: Mass supported by dashpot (damper) and spring Mass=M Damping Coefficient=c Spring Constant=K In both cases, derive the equations of motion...
  35. C

    Solve Damping Oscillation: Find Position Function of Spring

    Hello all, I want to find position function of a spring which is on a frictional surface so there is a friction force like k.m.g. Its differential equation is like that \ddot{x}+\omega ^2x=-kmg But I can't solve this. Can you help me to solve that equation? And also I don't understand...
  36. T

    Finding the damping ratio (zeta) of an nth order system from a transfer function

    I am having trouble with some of my homework. I am not quite sure how to find the damping ratio from a third order system when the transfer function (of s) is the only information supplied. Could anyone help me with this? I would like a method that would work with any nth order system...
  37. T

    Differential equation: Spring/Mass system of driven motion with damping

    Homework Statement A 32 pound weight stretches a spring 2 feet. The mass is then released from an initial position of 1 foot below the equilibrium position. The surrounding medium offers a damping force of 8 times the instantaneous velocity. Find the equation of motion if the mass is driven...
  38. K

    Direction of damping force on a surface

    Hi Suppose a particle is bouncing on a surface with a viscous damping coefficient... Question 1: The frictional force = -c(viscous damping coefficient)*v(velocity of the particle) But what is the direction of this force? Perpendicular [down] to surface? So if the surface is tilted at an...
  39. H

    How to Calculate Mechanical and Electromagnetic Damping?

    I will appreciate any contribtion to the question below. > You have a system that consists of a coil and magnet. The magnet, which is resting on a spring, is free to move up and down in the coil. This system can be modeled as a simple mass-spring-damper system with a...
  40. O

    What is the damping factor of a cantilever beam in free air?

    As part of some research work, I am reading a research paper which has taken damping factor of a cantilever beam c=0.01kg/ ms. With no background in advanced physics, I cannot understand how this assumption has been made. If you could tell me what's the damping factor of a cantilever beam in...
  41. S

    Spring Mass Damping System Question? Maximum acceleration?

    Spring Mass Damping System Question?? Maximum acceleration?? Homework Statement Hello, I was wondering if anyone knows how to go about answering these type of questions... Anti-vibration mounts are used to attach an instrument of mass 5kg to a panel. The panel is vibrating with an...
  42. L

    Neper freq, Damping factor, ratio, coefficient confusion.

    Hi all, this is my first post. I find a lot of conflicting definitions of damping factor, damping coefficient, and damping ratio on the internet, and in some textbooks, when related to RLC circuits. Sometimes I see the neper frequency described as the damping factor or damping coefficient...
  43. G

    Simp,e Harmonic Motion with Damping

    Hey, I have a simple question to ask. Some sources I have seen develop the solution for the underdamped case with an exponential term multiplied by a Cosine term. This is due to the application of the Euler identity to the solution with two exponentials each with one of the complex conjugate...
  44. F

    Free Vibration with Vicous Damping

    Hi, I am currently doing an experiment to determine the the viscous damping coefficient (c) of a dashpot. Where you move the position of the damper to determine the effect of the damping but my results show that when the damper is closer to the pivot the damping increases but i thought the...
  45. C

    What is the difference between electrical and mechnical damping factor?

    what is the difference between electrical and mechnical damping factor? what i mean is that, what is mean by electrical damping? the mechnical damping i know that is related to those frction, air resistance... how about electrical...
  46. D

    Solving for Damping Coefficient of Pendulum

    Homework Statement A 82.0 cm pendulum is released from a small angle. After 112 oscillations the amplitude is one half of its original value. The damping is proportional to the speed of the pendulum bob. Find the value of the damping coefficient, α, (in Hz). Homework Equations x =...
  47. U

    Damping term in Euler Bernoulli equation

    hello, I have made an FEM simulation of a cantilever beam in Matlab. I have included the damping using damping matrix C= alpha x M + beta x K. Problem is that I want to compare my result with this paper http://flyingv.ucsd.edu/rvazquez/Journal/nano.pdf (See eq.1) where the...
  48. C

    Power generation through building damping systems

    Hello, first time posting. If this is in the wrong forum, please move it to the correct one. (its a cross mechanical/structural/civil/electrical engineering idea) I was thinking on the way home Power generation. In order to generate power, wave motion can be used (such as tidal/wave power...
  49. F

    Finding spring constant, damping constant and Q for suspension of a car

    Homework Statement The suspension of a car (mass= 2000kg) sags a distance of 10cm when the weight of the entire car is placed on it. Also, the amplitude of its oscillations decrease by a factor of 50% over 3 complete oscillations. a) Find the spring constant(k) b) Find the damping constant(b)...
  50. D

    How to calculate the damping factor for a vibrating string?

    I'm running a finite element simulation of a vibrating guitar string, but I do not know how to calculate the correct damping factor for the string as it oscillates in air. I don't have information regarding how many times it will oscillate before the oscillation damps out, but I do have all the...
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