What is Damping ratio: Definition and 24 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. engnrshyckh

    Engineering Control system damping ratio

    I don't know how to calclute error in derivative for daming ratio of 0.5
  2. 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 =...
  3. W

    Parameters of a non-standard second-order transfer function

    For a standard second-order system, its transfer function is G(s) = ω2/(s2 + 2ζω + ω2) where ω is the natural frequency and ζ is the damping ratio. But for a non-standard second-order transfer function, G(s) = (2s + 1)/(s2 + 2s + 5), what are its natural frequency and damping ratio? Thank you!
  4. 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...
  5. A

    How to estimate a spring-mass-damper system's damping ratio?

    I have constructed a torsional balance, which basically consists of a torsional spring, and a damper. I model this as a spring mass damper system. And it is used to measure thrust of some propulsion system. This is how the system looks like. I am just very eager to find out, how to model the...
  6. S

    Calculate gain of a transfer function without root locus

    Hi, Having a bit of trouble with this question: "Assuming a proportional controller is used, determine the gain to achieve a damping ratio of 0.5, for the following transfer function. Hence calculate the associated natural frequency and oscillation period. G(s) = -4(s+0.4) / s^2+1.6s+14." I...
  7. H

    Selecting Appropriate Damper

    I've been a bit lost figuring out what damper I should be using for the front suspension I am designing. Right now I'm running a wheel rate of 60 lbf/in at the front with a ride frequency of 1.2254 Hz. The front is also supporting a sprung mass of 391.68 lbf. Comfort is the end requirement of...
  8. D

    Overshoot of 15% what is damping ratio

    Homework Statement A shock absorber is to be designed to limit its overshoot to ##15## percent of its initial displacement when released. Find the damping ratio ##\zeta_0## required.Homework EquationsThe Attempt at a Solution My question is since log decrement, ##\delta = \ln\frac{x_1}{x_2} =...
  9. S

    Calculating Damping Ratio of SMAs Using Hysteresis Loops

    G'day guys, I am currently trying to calculate the damping ratio for Shape memory alloys using hysteresis loops. The damping ratio is usually represented as ΔU/2∏U, where ΔU is the energy lost due to material damping and U is the elastic strain energy. My problem is trying to find this...
  10. B

    Damping ratio from Eddy current breaking

    Hello All, I have been asked to design and build a rig that will introduce the concept of a mass spring damper system to mechanical engineers in their early years of university. To make it slightly more complex, the rig needs to be torsional rather than linear. My design so far is to use a...
  11. C

    Estimating the damping ratio from the waveform graph

    Homework Statement From the waveform shown below, estimate a) the damping ratio ζ (you may compare response with a standard chart); b) the forced or damped frequency of oscillation; and c) the natural or undamped frequency of oscillation. Homework Equations Since the waveform is under...
  12. V

    Closed loop damping ratio

    From control systems: I am asked to find the value of K that gives the closed loop damping ratio of 1/sqrt2. The value for the complimentary sensitivity is T(S)=(2KS +4K)/(s^3 +162S^2 +(320+2K)S +4K) so how do I find the value for K? I tried putting it in the general equation, but it...
  13. R

    How to find damping ratio, revision questions.

    Hi guys, Revision for an exam tomorrow, I hope someone can help? I've been given the answers but I can't work out how to find the damping ratio without being given a velocity or distance for the mass to travel?A mass of 6kg is suspended on a spring and set oscillating. it is observed that...
  14. 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...
  15. 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...
  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. 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?
  18. 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...
  19. S

    Damping ratio from transfer function

    I have a transfer function for system. 23.23*s + 1.421 ------------------------------------- = tf s^2 + 25.88*s + 1.421 Since the numerator has a non-zero coefficient for "s" I am wary about equating 25.88 = 2 * zeta * omega [the stuff we usually do for calculating the damping...
  20. S

    Damping ratio from a transfer function

    I have a transfer function for system. 23.23*s + 1.421 ------------------------------------- = tf s^2 + 25.88*s + 1.421Since the numerator has a non-zero coefficient for "s" I am wary about equating 25.88 = 2 * zeta * omega [the stuff we usually do for...
  21. S

    Given a curve how to find the damping ratio?

    I have a data of a system (2nd order spring-mass-damper). From the looks of it, the system is quite certainly overdamped. Can someone guide me as to how to find the damping ratio? Regards, -sgsawant
  22. E

    Determining Damping Ratio for Spring-Damper System

    Hi, my question is about determining the damping ratio for the upper spring-damper part of the system given in the link. Is it still r2/(2*sqrt(k2*m2)) or something equivalent should be determined? http://img217.imageshack.us/img217/3148/sprdampmass.png [Broken] Thank you!
  23. S

    Gilbert Damping Ratio in Ferromagnets

    Does anyone know the highest alpha (Gilbert damping ratio) you could get on ferromagnets? People for various reasons aim for the lowest alpha and it is around 0.008 these days (dimensionless). But I need to know whether higher values are possible or not. A brief reminder on what alpha is: It...
  24. M

    Relationship of Critical Damping Ratio in Elastomers

    Hi guys, working a project where I need to guess the damping ratio (used for a numerical analysis) based on other properties of a material. We're looking to use an RTV as a vibration damper (we don't need a lot) but I can't seem to get any vibrational properties (called Honeywell, Dupond...
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