What is Damping coefficient: Definition and 28 Discussions

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. 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...
  2. P

    Damping coefficient in RLC model (piezoelectric transducer)

    Hello! I am a university student working on a project regarding a piezoelectric patch transducer, and RLC modelling of said transducer. Edit: After reading the rule post i think i should clarify this is not coursework homework, this is a thesis project. The short version of my question is how...
  3. B

    Natural Frequency & damping coefficient from transfer function

    Homework Statement Here is the transfer function of a buck converter I derived: What I need to do next is obtain equations for w0 and ζ. I know how to do this for equations that follow the general form: But in this case I just can't figure out exactly how to do it. How do I find a...
  4. V

    Damping coefficient in damping mechanisms

    Hello everyone, I am trying to design an element that its purpose is providing stiffness and damping. The material that I wish to use is rubber. My question is, how can we calculate the damping coefficient (c) for the calculation of the term c*dx/dt, when we know the loss factor of the...
  5. Chrono G. Xay

    Can We Predict Damping Coefficient of a String Using Mathematical Simulation?

    Is it possible to predict the damping coefficient of a string using a mathematical simulation that included the string's diameter, length, frequency (and therefore tension), material density, and elastic modulus (if not also its Poisson's ratio) as opposed to simply looking at the amplitudes of...
  6. S

    What Are the Correct Formulations for the Damping Coefficient?

    Hi, I have been looking for formulae for the damping coefficient, and I found two different formulae for it. http://www.xyobalancer.com/xyo-balancer-blog/viscous-damping-coefficient This webpage states that damping force, Fd is given by Fd=-cv, where c is the damping coefficient while v is the...
  7. K

    Relationship between surface area and damping coefficient

    I have been investigating the damping of an oscillating mass on a spring by a piece of card of varying surface area, in order to work out the damping constant λ for the equation y = A₀ e-λt sin(ωt). I took the natural log of the amplitude of each successive oscillation and plotting that against...
  8. gfd43tg

    Damping Coefficient and Resonant Frequency of a 2nd order circuit

    Hello, I am having major confusion for how to find the damping coefficient, α, and the resonance frequency, ωo, for a second order circuit, in general. I know that there are tables for standard circuits like a series RLC and parallel RLC giving those values, but I am certain that I need to know...
  9. J

    Calculate damping coefficient of dashpot from physical dimensions

    Hi all, I am trying to calculate the damping coefficient of a linear viscous dashpot/damper given the dimensions of the piston, and the dynamic viscosity of the damping fluid. I have found this calculator, but does anyone know the equation that it uses...
  10. B

    What is the role of roll damping coefficient in aircraft performance?

    Hello, I am new to Aerodynamics and am having trouble understanding what exactly the roll damping derivative is. The roll damping derivative is a measure of the change in rolling moment coefficient with respect to nondimensional roll rate and is usually negative. Does that mean a glider...
  11. H

    Find damping coefficient at a given vibration mode

    I am working on a motorcycle dynamics problem. I have written the equations of motion in matrix form in MATLAB (and mathcad). It is a 4 degree of freedom system, so I have a mass, damping and stiffness matrix all 4X4. I am able to find from these matrices the natural frequencies, and damping...
  12. 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...
  13. 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...
  14. 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...
  15. 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 =...
  16. A

    How Is the Damping Coefficient Calculated in a Fluid-Dynamic Dashpot System?

    So have a loose fitting piston attached to a conrod, attached to a flywheel. The chamber the piston is in is sealed reasonably well around the controd, and is full of a fluid with a viscosity. Let's say the flywheel is spinning. I want to work out from the fluid dynamics occurring, what the...
  17. I

    Does the Mass Affect the Damping Coefficient in Spring Oscillations?

    Just a quick question that I am unsure about. Let say a vertically suspended spring with an attached mass at the bottom. How does the mass relate to the damping coefficient? I am guessing that the mass is proportional to the damping coefficient. The heavy the mass at the end, the higher the...
  18. S

    Finding damping coefficient of material

    i have found the damping factor of a plate from experimental vibration. how can i find the damping coefficient of the material of the plate
  19. P

    Vibration Isolation Damping Coefficient

    Homework Statement I am trying to solve how to select a vibration isolator for a machine to be mounted on a vibrating surface. I know the disturbance frequency, 22.5Hz and the mass of the machine is 40kg. I have selected some commercially available rubber isolators and subsequently know their...
  20. A

    Calculate the damping coefficient of air

    So I am trying to calculate the damping coefficient of air passing around a piston that is oscillating in a tube. The idea is completely theoretical. I don't have any real data. As far as i understand: 1. The viscous sheer stress = mu.du/dy 2. Therefore the viscous sheer force = (piston...
  21. B

    Calculating Damping Coefficient for Spring Length 36.3mm, Load Mass 0.036kg

    Homework Statement I want to find the damping coefficient of a spring of free length 36.3mm, with load mass of 0.036kg. Homework Equations i need the amplitude of this system, i have the angular frequency, but not the damping ratio. So i was trying to use the formula: damping...
  22. D

    Damped oscillations - Finding damping coefficient

    Homework Statement A 50.0g hard-boiled egg moves on the end of a spring with force constant k = 25.0 N/m. It is released with an amplitude 0.300m. A damping force Fx = -bv acts on the egg. After it oscillates for 5.00s, the amplitude of the motion has decreased to 0.100m. Calculate the...
  23. W

    How do I get the damping coefficient experimentally

    Homework Statement This problem is part of my project for Controls 3B. The project revolves around modeling a bouncing ball that is dropped from a certain height and bounces of the ground. I have been told to use the mass-spring-damper model to simulate the ball while it is in contact with...
  24. F

    Find the value of the damping coefficient

    Homework Statement A 95.0 cm pendulum is released from a small angle. After 115 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. Homework Equations b=sqrt k*m A=...
  25. J

    Dynamics-Critical Damping Coefficient

    I have been reading Equations of Motion pertaining to "Damped Single Degree of Freedom Systems" There, the critical damping coefficient wherein the oscillation is completely eliminated from the system is defined by: Critical Damping Coefficient = 2 x m x (omega) where, m=mass...
  26. D

    SHM damping coefficient which envelope sign?

    Hi, I'll get right away to the point. I'm determining damping coefficients from motion sensor traces of a damped oscillator. I have gone through the standard procedure of taking natural logs of the sine wave peaks and drawing graphs etc, however what puzzles me is that the SIGN of the damping...
  27. J

    What is the formula for calculating drag on spherical objects in laminar flow?

    Hi I'm looking for a place were I can find the damping coefficient for water. Maybe someone has/can find/knows a good site/table/url? thank you
  28. M

    Calculate Damping Coefficient of 50.0g Egg

    A 50.0-g hard-boiled egg moves on the end of a spring with force constant . It is released with an amplitude 0.300 m. A damping force acts on the egg. After it oscillates for 5.00 s, the amplitude of the motion has decreased to 0.100 m.Calculate the magnitude of the damping coefficient ...