What is Damping: Definition and 307 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. I

    What is the differential equation model for this Mass Spring Damping system?

    Homework Statement That is the system. B1 and B2 are the dampers I am asked to obtain the differential equation model for the system. I haven't dealt with these in a while so I'm not sure where to start. Homework Equations Like I stated earlier i haven't messed with one of these in a...
  2. E

    Velocity feedback damping in aircraft

    Describe velocity feedback damping in relation to aircraft systems? my attempt at an answer: I know what damping is, and i know what velocity feedback is, I just can see how they fit together. I think it's something along the lines of; an auxilery power unit has a speed sensor...
  3. A

    Dashpot Damping Coefficient

    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...
  4. 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...
  5. W

    Driven oscillator with damping

    Homework Statement The oscillator is driven by a force F(t) = mAcos(wt). Plot the amplitude D of oscillations, in units of the maximum (resonant) amplitude D(max), as a function of w in units of w_0. (In other words, plot D/D(max) versus w/w_0.) Find Q. \beta=(1/6)w_0 Homework...
  6. A

    Resonance - working out damping constant and damping factor

    Homework Statement I'm doing a lab report on resonance and I'm trying to find the damping constant and damping factor. I measured as many amplitudes(A) for successive oscillations as possible and graphed amplitude number (n) vs. ln(A) The hint read: Part 1:Using equation 5, Plot a graph...
  7. P

    Coefficient of restitution and damping

    Can someone please explain me the difference between damping and Coefficient of restitution (COR)? Are both the same or how do they relate to each other? Thank you,
  8. 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
  9. 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...
  10. 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...
  11. U

    Differential Equations: Is there Damping?

    Homework Statement A spring mass system has the equation of motion: c1e^(-t)*sin(t) + c2e^(-t)*cos(t) + 3*sin(t) Is there damping in the system? Is there resonance in the system? The Attempt at a Solution If I had to guess I would say that the 3*sin(t) at the end of the equation...
  12. B

    Solving Linear Damping Model Homework

    Homework Statement I am asked to write down the equation of motion of m with respect to O, hence show that x(t) satisfies the differential equation. m\ddot{x}+r\dot{x}+kx=mg+kl_0+m\ddot{y} See attached diagram. Homework Equations I have the force of the spring H, the Damping R and the...
  13. 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
  14. D

    Find the damping constant of the Pendulum

    Homework Statement A physical pendulum consists of a uniform sphere with radius r=2.5cm and mass M = 0.5kg attached to a uniform rod with length L = 1m and mass m=250g The friction of the suspension and air moderately reduce the amplitude of oscillation by factor of 2 in 19.6s. What is the...
  15. S

    Does damping of period affect the period?

    Hi there, Sorry typo in the title and I can't figure out how to change it! I am just wondering if anyone can help me - does damping (drag) increase the period of a pendulum? As opposed to if it was in a vacuum? I have been trying to figure this out for some time - I know that drag is dependent...
  16. 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...
  17. 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...
  18. T

    Mass/Spring System Damping Constant

    A mass weighing 32 pounds stretches a spring 6 inches. The spring constant is equal to 64 lb/ft.The mass moves through a medium offering a damping force that is numerically equal to \beta times the instantaneous velocity. Determine the values of \beta>0 for which the spring/mass system will...
  19. V

    Finding the damping constant from SHM

    Homework Statement I doing a investigation coursework at the moment for physics A2. I am investigating how the viscosity of oil is affected by the temperature. I am attemping to prove the viscosity decreasing by showing that the damping constant decreases. I have attached a excel workbook...
  20. Y

    Question of damping vibrating strings

    This is not homework, I need someone to verify (9) and (10) below whether I am correct because I don't have the answer. I need to find the solution of the following: Question Find the solution of the equation for damping vibration string stretched from x=0 to x=L where \frac{\partial ^2...
  21. 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 Thank you!
  22. T

    Finding Viscous Damping Constamt

    Homework Statement I am working with a problem of damped harmonic motion. I am given that the motion is in a medium that exerts a force of 2N when the speed is 4 cm/s. The mass is 5kg. Homework Equations C = F/v The Attempt at a Solution I thought that the viscous damping...
  23. M

    Damping due to porous plate travelling through hydraulic oil

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  24. A

    Pulsation damping in a heat engine

    Hi all, I have recently been shown a diagram of pressure versus piston position for a particular heat engine. The system is based on a Joule cycle and is designed to take a drive stroke at constant pressure. Now what I'm trying to understand is, the pressure appears to 'wobble' slightly...
  25. D

    Two coupled harmonic oscillator, damping each other

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  26. A

    Calculating a Damping Constant

    I am given the following information: A 2.20 kg mass oscillates on a spring of force constant 250.0 N/m with a period of 0.615 s, and I am asked to find the damping constant. Can someone tell me what equation to use?
  27. F

    How Many Oscillations to Reduce Amplitude by 1000 in a Damped System?

    Homework Statement A mass spring system has the following parameters: damping constant is 1.00 Ns/m spring constant is 1.00N/m and mass is 1.00 kg The mass is displaced from equilibrium and released. Through what minimum number of oscillations must the mass move in order to reduce the...
  28. S

    Gilbert Damping Ratio in Ferromagnets

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  29. H

    Amplitude damping with harmonic oscillators

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  30. F

    Motion with damping constant

    Homework Statement I'm a little ashamed to post this, because I bet I'm missing something obvious, so try not to laugh... A freely rolling freight car weighing 10^4 kg arrives at the end of it's track with a speed of 2 m/s. At the end of he track is a snubber consisting of a firmly anchored...
  31. L

    Building an rc chopper and have a question to do with damping vibrarions

    I have already built most of the chopper but am trying to add an accelerometer. Let's say the blade is rotating at 600rpm, this is causing vibrations throughout the vehicle at 10hz. I want to make a compartment which doesn't feel most of these vibrations. I'm thinking of building something using...
  32. T

    Damping , resonance and natural frequency?

    When a forced oscillation is damped, it is true that the frequency at which resonance occurs decreases right? so does this mean that the natural frequency has decreased too or does it only mean that resonance does not occur at natural frequency when being damped?
  33. D

    Critical Damping in Multi-Modal Resonant System

    Let's say I have a system with multiple oscillatory modes. Is it possible to have anything in this system that resembles critical damping?
  34. C

    Integrating angular damping into angular velocity and rotation

    I'm using a 3rd party physics engine to run rigid body physics. It just updates the bodies once every 16 ms or so. I'm trying to write an algorithm to predict where free-falling bodies will be in 2 seconds using standard physics equations. I'm having trouble with predicting angular velocity and...
  35. 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...
  36. 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...
  37. V

    Nutational damping in satellites

    i want to ask ...how can i model sloshing of fuel in satellite feul tank , to an energy sink model... can anybody help me?
  38. M

    Vibration Damping an Analytical Scale

    Hello MechEs (or anybody else who'd care to reply) I'm about to get a small, but fairly sensitive analytical scale recently (down to 0.01 mg) and now I'm trying to figure out a way to dampen ambient vibration from the room and its surroundings (people walking around, HVAC, etc.) I've got a...
  39. T

    How to calculate viscous damping properties of air in loudspeaker design

    In the design of a loudspeaker, one intuitively seeks a critically damped alignment. We must consider the electrical resistance of the coil, magnetic field strength, mechanical resistance, mechanical compliance, and mass (diaphragm + acoustic load) of the system. The electrical resistance...
  40. R

    Mechanical damping practical use ?

    im supposed to write a little discussion on mechanical damping practical use...can anyone give me a proper website or note in the internet.....
  41. 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...
  42. H

    Bicycle Rear Shock damping coefficent

    Just carrying out calculations on a rear bicycle shock. Got my hands on one and intended to calculate spring stiffness and damping coefficent practically. Did it on the spring using a tensile tester and have come up with a spring stiffness value of 130000 n/m2. (750 lb/in). Problem when i...
  43. L

    Damping effect of swinging pendulum affect period?

    Lets say i have a magnetic pendulm, (basically a barmagnet suspended from a with a string tabletop) and a conductor at the bottom. The conductor will ofcourse have Foucault currents generated in it, and this due to conservation of energy, will slow down the swinging of the pendulum, reducing...
  44. G

    Fluid Dynamics, Calculating viscosity using damping coeffiecient

    Homework Statement Hello, I am doing a project which requires damping and have decided to use some viscous damping. It is simply on a hacksaw blade with a weight on the end. Therefore, other than just trial and error I would like to calculate the range of viscosities that may be useful for...
  45. A

    Damping in Duffing driven-anharmonic oscillator

    Greeting every one. In Duffing equation, the damping coeffecient usually assume possitive values (<<1). However, at certain cases, the damping coeffecient may asume negative values. Can anyone explain the meaning of positive and negative damping in Duffing equation as well as in real physical...
  46. Q_Goest

    Another non-viscous damping thread

    I have a reciprocating pump running 350 RPM, 2.25" stroke. Piston is double acting (ie: force in both directions). Load is ~30,000 pounds. There's a very small clearance in the coupling between piston and drive train, and this coupling goes through the same motions as the piston (it is...
  47. Q

    Modeling Non-Viscous Damping with DE

    im trying to model a mass hitting a block of honeycomb aluminum with a DE. is the whole mx"+bx'+kx=F(t) eqn. void because b isn't viscous? Is there a way to get around that?
  48. H

    Damping Oscillation Homework: Time Constant & Amplitude After 4s

    Homework Statement A small earthquake starts a lamppost vibrating back and forth. The amplitude of the vibration of the top of the lamppost is 6.5 cm at the moment the quake stops, and 8.0s later it is 1.8 cm. What was the time constant for the damping of oscillation? What's the...
  49. Z

    What is the Damping Constant for a Spring in Sea Water?

    Hi, I am working on a problem with a free hanging mass attached to a spring and damper in parallel. I believe my system equation is as follows: my'' = mg - by' - ky My questions: 1) It has been a while since I've taken this course and just wanted to confirm I wrote my system...
  50. N

    Amplitude of oscillations depends on the amount of damping?

    Which one of the following statements about an oscillating mechanical system at resonance, when it oscillates with a constant amplitude, is not correct? A The amplitude of oscillations depends on the amount of damping. B The frequency of the applied force is the same as the natural frequency...
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