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. Bossmand Per

    A Modeling the damping of a physical rigid pendulum

    I'm engaged in a research project focused on pendulums. I'm trying to model a rigid pendulum's motion with a second order differential equation (where time is the independent variable) describing the relationship between θ (theta) , ω (omega) and α (alpha) where: - θ is the angle of the...
  2. S

    Modelling a spring system with damping force and external forces

    I think its critically damped by looking at the graph of the solution.
  3. SamuuLau

    I The effect of temperature on the damping of a guitar string

    I am a high school student and recently I have been working on a project about how temperature affects the frequency of a string emits. I have read blogs like https://www.physicsforums.com/threads/tension-and-frequency-with-change-in-temperature.833185/ and completed the part of thermal...
  4. M

    Damping and friction in syringe equation of motion

    Hello Everyone I want to model forces affecting on syringe plunger , but I do not know how to calculate terms like friction and damping coefficient. What I imagine is that : F_driving = ma + cv + f ----------------(1) where: f: friction c: coefficient of viscous damping m: mass of plunger (is...
  5. daanisrael

    I How is the damping of sound (over distance) affected by air properties?

    Hey all, For my physics major I need to quantify the acoustic effect of sunfields. I'm trying to do this by measuring the sound level before and after a sunfield, and after that by measuring a comparable situation, only without a sunfield. By comparing the results of the two measurements I'll...
  6. Pipsqueakalchemist

    Vibration: Transmissibility ratio sign change when damping is equal to zero

    So for the transmissibility ratio equation, after doing a lot of questions when damping is zero and I have to take the square root of the denominator. Some questions take the positive root (1-r^2) while for other questions the solution takes the negative root (r^2-1). Can someone explain when we...
  7. VVS2000

    I Damping in a coupled pendulum system

    http://www.cts.iitkgp.ac.in/Phy_1st/Lab_WorkBook/CoupledPendula.pdf This is similar to the experiment which I did
  8. P

    Where does the equation C=2*sqrt(km) for Critical Damping come from?

    Im using this equation to find the damping from a ruler cantilever experiment. Any information about what critical damping really means and how it reflects in a ruler cantilever is also really helpful. Thank you again.
  9. A

    Engineering Book considering FEM analysis for complex eigenvalues (incl. damping)

    Can anyone recommend a book in which complex eigenvalue problems are treated? I mean the FEM analysis and the theory behind it. These are eigenvalue problems which include damping. I think that it is used for composite materials and/or airplane engineering (maybe wing fluttering?).
  10. M

    I Build Setup to Create Electric Damping Force

    Hello! Is it possible to build a setup (containing time dependent and independent electric fields), such that a charged particle will feel a force proportional to its velocity i.e. ##ma = -\alpha v##?
  11. Shreya

    Is w Constant in Damped Oscillations?

    My first intuition is that for small damping Fd<<Fr
  12. maistral

    A Backward Euler technique vs. periodic function: Damping out?

    So I've been programming the BDF methods and for some reason I have an issue with the Backward Euler technique. Given the differential equation y" + y = 0 (with y(0) = 2, y'(0) = 0), my backward Euler solution goes like this: Obviously this is not possible as the function should be a...
  13. dRic2

    I What Happens to Energy When Phonons are Damped?

    If you go beyond the harmonic approximation, phonons can not be thought as independent quasiparticles anymore and phonon-phonon interactions are taken into account. This eventually translates into the fact that phonons frequencies get renormalized ( ##\omega \rightarrow \omega^′ +i\nu ##)...
  14. J

    Waves - General question about Damping and how it affects a propagating wave

    I think increasing the damping would decrease the amplitude and increase the Period (T). But, what I'm really unsure about is the frequency, wavelength and wave speed. Would it be no effect on those three? Because if dampening acts like friction, wouldn't it slow down the wave/ increase speed?
  15. T

    Equation of a sound wave with viscous damping in ideal gas

    How can we find a equation of a 1D sound wave in a non-differential form in an ideal gas with viscosity? How does the damping work? How does the wave lose energy at each layer as it propagates? To be clear I am looking for a simple exponential-sinusoidal function for it just in the case of...
  16. LCSphysicist

    Devise two damping mechanisms for these coupled pendulums

    ] I am not sure how i could begin, someone can help me? In the first mode we have a spring not stretched, while in the second, is not only stretched but the balls are outing of phase by 180 ° too.
  17. engnrshyckh

    Engineering What is the Correct Interpretation of Damping Ratio in Control Systems?

    I don't know how to calclute error in derivative for daming ratio of 0.5
  18. J

    What Is the Default Damping Value in PhET's Masses and Springs Simulation?

    PhET: https://phet.colorado.edu/en/simulation/masses-and-springs Any information would be appreciated. Thanks in advance!
  19. L

    Solving for the Damping Constant

    ##x(t)=x_m e^{\frac{-bt}{2m}}cos(ωt+φ)## Damping Factor: ##e^{\frac{-bt}{2m}}## (##b## is the damping constant) Estimated ##ω##: ##\sqrt{\frac{k}{m}}## More Accurate ##ω'##: ##\sqrt{\frac{k}{m}-\frac{b^2}{4m^2}}## Also: ##T = \frac{2π}{ω}## and ##F = kx##. So, my answers: ##k = \frac{Mg}{4x}##...
  20. Boltzman Oscillation

    Engineering Measuring the damping frequency from an oscilloscope reading

    I know the following equations for if the damping ratio is less than 1: $$\sigma = -\zeta \omega_n$$ $$\omega = \sqrt{(1 - \zeta ^2)\omega^2_n}$$ I am given the following circuit that I built on LTSpice: Measuring the voltage between node 2 and ground (blue), and the voltage Vc4(t) (green) I...
  21. Boltzman Oscillation

    Engineering Help finding the damping ratio formula for this circuit

    The circuit to be analyzed is shown below: Since initial conditions are zero (from the instructions) I will use laplace transforms for the cirucit and I will use the MAME method to solve this circuit. The laplace transforms that are required will give me: $$E_g(s) = \frac{10}{s}$$ $$ L_3 =...
  22. M

    MATLAB No damping but the solution to simple harmonic oscillator damps?

    I posted yesterday but figured it out; however, a different issue I just detected with the same code arose: namely, why does the solution damp here for an undamped simple harmonic oscillator? I know the exact solution is ##\cos (5\sqrt 2 t)##. global delta alpha beta gamma OMEG delta =...
  23. Q

    I I computing the CMB Damping Tail

    The formula for the Damping Tail in the CMB BAO analysis generally has the form: $$\mathcal{D} (k)=\int_{0}^{\eta_0}\dot\tau e^{-\left[\frac {k}{k_D(\eta)} \right]^2}d\eta $$I can’t make sense of this. ##\dot\tau## is the Thompson (Differential) Opacity; the product of electron density, cross...
  24. J

    I Wave damping on a stretched string

    Is there a simple model I can use to describe the damping of a wave on a string? Is c = 2*mu*sqrt(T/mu) where mu is damping coefficient, mu is linear density and T is tension a valid option? I replaced k and m with T and mu from the simple equation found here. What I am interested in showing is...
  25. Q

    What Is Landau Damping and Why Is It Important in Plasma Physics?

    I have no clear idea of this phenomenon?
  26. K

    Noisy Chiller: Solutions to Reduce Vibrations

    Dear forum members, We have a water cooled chiller device (see its model in attached link) and we use it to cool a hot mirror element. Unfortunately the chiller is vibrating and the vibrations couple all the way to the mirror through a pair of rubber tubes (1cm in diameter, 2m in length) and a...
  27. N

    Lenz's Law for a rotating PM motor rotor spinning in a thin CU tube

    The motor is required to operate at its resonance frequency and I am looking to add a thin-walled (0.010") copper tube inside the stator bore to add some damping. The current motor air-gap is 0.015". If I install a copper tube in the stator bore bonded to the stator and leave a 0.005" air-gap...
  28. Protea Grandiceps

    I X variable in damping force equation for damped oscillation?

    Hi, for ease of reference this posting is segmented into : 1. Background 2. Focus 3. Question 1. Background: Regarding (one, linear, second-order, homogeneous, ordinary, differential) equation describing the force in a non-driven, damped oscillation: F = m.a = -k.x - b.v F =...
  29. M

    Help with Damping Questions: How to Start & Learn More

    Hello everyone, I am really stuck on the first question in the document and I don't even know where to begin. If someone could explain what is happening and how to start the problem, I am confident I will be able to tackle it. It would also be a big help if you could direct me to some...
  30. R

    Damping a trampoline on the 2nd floor

    My son has autism. He is 15 and weighs 235 pounds. He is also 6 feet tall. He loves to jump on his trampoline in our living room, yeah I have a trampoline in my living room. We live on the 2nd floor of an apartment. I noticed the ceiling in my downstairs neighbor's home bending a little every...
  31. I

    Finding the damping force for a critically damped oscillator

    Homework Statement A critically damped simple harmonic oscillator starts from an amplitude of 5.0 cm and comes to rest at equilibrium 3.5 s later. The SHO is made of a 0.58 kg mass hanging from a spring with spring constant 150 N/m. Assuming the friction force is in the vertical direction, how...
  32. R

    LRC Series Circuit Critical Damping

    Homework Statement Homework EquationsThe Attempt at a Solution My attempted solution is above and here https://imgur.com/8RmDMf8/ I'm confused as to the answers in the book being i and iii (I just don't see how i is included). If critical damping occurs at the value above, and if you go above...
  33. SuchBants

    Finding the max frequency of a driven oscillator

    So I've derived the equation for the amplitude of a driven oscillator as: \huge A=\frac{F}{m\sqrt{(\omega_{0}^{2}-\omega_{d}^{2})^{2}+4\gamma^{2}\omega_{d}^{2}}} Which is what my lecturer has written. Then taking the derivative and setting it to 0 to get the turning point. He makes this leap...
  34. G

    Weak Damping - how to relate the amplitude and phase difference

    Homework Statement Derive the relationship bewteen x_{max}, A_{+}, A_{-} and \phi Homework Equations x(t) = e^{\gamma t}(A_{+}e^{i \omega_d t} + A_{-}e^{-i \omega_d t}) x(t) = x_{max} e^{\gamma t} cos(\omega_d t + \phi) The Attempt at a Solution I know the e^{\gamma t} cancels and for the...
  35. S

    Automotive Estimation of the damping coefficient of a suspenion

    Hi all, I have a suspended seat with a scissor mechanism like the following: This seat is composed of coil spring and a hydraulic damper. My aim is to develop a multibody model of that seat. Actually, my model is quite complete, only the parameters of damper are missing (i.e. the damping...
  36. Jozefina Gramatikova

    Simple harmonic motion - damping introduced

    Homework Statement Homework Equations [/B]The Attempt at a Solution I can solve everything but d). Please help
  37. WeiShan Ng

    [Calc] Sign Convention in damping spring system

    Homework Statement A carriage is mounted on a spring, as shown in the diagram. The bottom of the spring is fixed to the ground. The carriage (loaded with its passenger) has a mass of 150kg. The carriage can only move vertically. The natural length of the spring is 10m and its spring...
  38. SuchBants

    Estimate Decay Coefficient in Ae^-at Graph

    Homework Statement How can I estimate the decay coefficient in Ae^-at for this graph I know the equilibrium position Homework Equations damped oscillation The Attempt at a Solution not sure if this is right.[/B]
  39. S

    DIY Vibration Measurement Device for Engineers using Flex Sensors

    Hi, I need something that would measure vibrations along an axis, so instead of buying a bunch of accelerometers I thought I’d quickly make smth myself. I’m majoring in engineering and not physics, so while I have no problems with the construction, I’m kind of stuck with the physics aspect. I...
  40. T

    A What was so extraordinary about Landau damping?

    I've been told Landau damping was a surprising phenomenon that many people didn't believe possible when first introduced since it permit wave damping in the absence of collisions. I appear to be missing something fairly basic and fundamental to this picture, but aren't all wave-particle...
  41. nabs16

    Damping effect in piezoelectric energy harvesting systems

    Hi, I have to make a report on an energy harvesting system using piezolectric materials by comparing two methods each other which are: the standard technique (rectifier bridge+filtering capacitance) and the nonlinear technique, by adding to the standard device a switch and an inductor in...
  42. Physics345

    Explaining Damping with a car's suspension

    Homework Statement Explain what is meant by damping. Choose a specific technology that requires a damping mechanism and describe how the damping takes place. Homework Equations none The Attempt at a Solution Damping is to reduce amount of friction being caused from oscillations, therefore...
  43. O

    How to model a non-linear pendulum with air resistance?

    Homework Statement I have found a differential equation that models a non-linear pendulum with air resistance, and now I have data. I've looked at the following site for guidance on how to analyse the data. It compares the motion of a damped spring, and compares it to the motion of a damped...
  44. T

    I Why do we need to use causality arguments in the Landau damping problem?

    Related to Figure 8.4 the author mentions this when stating (8.25): "Note that the semi-circle deviates below the real -axis, rather than above, because the integral is calculated by letting the pole approach the axis from the upper half-plane in -space." Why is the pole calculated in this way...
  45. J

    New time constant to change damping ratio

    Homework Statement Homework Equations Time constant = 1/ξwn The Attempt at a Solution Time constant = 1/ξwn Damping factor = ξwn So T = 1/ξwn If ξwn is reduced by factor of 2, then Time constant must be increased by factor of 2. So Answer is: B Book answer is A How? p.s. I know I'm posting...
  46. AbigailG

    Finding Amplitude of spring oscillation after damping

    Homework Statement [/B] A spring with spring constant 10.5 N/m hangs from the ceiling. A 520 g ball is attached to the spring and allowed to come to rest. It is then pulled down 6.20 cm and released. What is the time constant if the ball's amplitude has decreased to 2.70 cm after 60.0...
  47. M

    Sizing of a damping - spring - mass system

    Hello All, I have come across a problem, which has troubled me for some time now. What needs to be done is the following: A mass on a rod 0.6m (mass less) has a mass of 1 kgr attached at the end of it. The rod needs to be rotated 60 degrees, within t=120 sec (see image). What I would like to...
  48. H

    What is the best material for low damping in a racing simulator pedal set?

    Cross posted this in the materials forum but i received nothing so I'm posting it here. << Mentor Note -- OP has been reminded not to cross-post at the PF >> So the application is in a pedal set for a racing simulator cockpit. The brake pedal has a high resolution pressure transducer that...
  49. JTC

    A Where Can I Find a Tutorial Animation for Damping of a 1D Oscillator?

    (I list this as Advanced because the question is not what it seems from the title.) So most know the cases: no damping, underdamping, critical damping, overdamping. I got that: this is not a request for explanation. Rather... Does anyone know of a web page that has some tutorial ANIMATION...
  50. L

    Methods for Damping High Frequencies in FEM Thin Film Model?

    I would like to simulate the vibrations of a thin film polymer in vacuum using nonlinear analysis. For this purpose I am using an FEM program I have written in MATLAB. I do not have any data regarding damping in the structure, so I am estimating the damping using stiffness-proportional-only...
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