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. S

    How Do You Determine the Damping Constant from an Amplitude vs Time Graph?

    how can we find damping constant from graph of amplitude versus time?
  2. F

    What Is the Minimum Damping Constant to Limit Vibration Amplitude to 3.2 mm?

    Homework Statement A sensitive instrument with the mass of 30 kg should be installed in a labratory. In the labratory, there exist a machine that causes the floor to vibrate with the frequency of 0.8 Hz and with the amplitude 8.0 mm, each with the spring constant k = 500 N/m. Its then...
  3. K

    Critical damping vs overdamping

    why critical damping and over damping doesn't undergo oscillations?
  4. 1

    How can a part's geometry be used for damping or to reduce vibration?

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  5. S

    Damping Properties of Rubber: Understanding the Impact of Strain Amplitude

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  6. PsychonautQQ

    Damping factor in critical damping

    The position equation for a oscillator undergoing critical damping is given by x(t) = Ate^(-γt) + Be^(-γt) where γ = c/2m and c is from the original force equation ma + cv + kx = 0 γ is called the damping factor my book then goes on to say without explanation that γ = c/2m =...
  7. R

    What Constant c Achieves Critical Damping?

    Homework Statement Suppose a mass- spring is modeled by x''+ cx'+100x. What should the damping constant c be in order that critical damping occurs? Homework Equations The Attempt at a Solution I set the discriminant equal to zero so that there are real repeated roots. B^2-4ac=0...
  8. 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...
  9. E

    How Do You Calculate the Damping Constant in a Sloped Car Scenario?

    This is actually for a engineering course in modelling, and not in physics per se, but it seems to me to be fairly basic physics. Apologies in advance if it's out of place. Homework Statement A car with a mass of 1000 kg is held still on a slope with an inclination of 5.8 °, and then let...
  10. A

    Forced SHM with damping problem

    Homework Statement A mass, m, attached to a spring hangs vertically downwards under gravity. It is subject to a viscous damping force proportional to its velocity. The spring constant is k > 0. A periodic force is applied to the spring and the equation of motion for the mass is \ddot x+...
  11. 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...
  12. A

    DE: Critical Damping Oscillating?

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  13. J

    Calculate damping coefficient of dashpot from physical dimensions

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  14. W

    Electromagnetic damping logarithmic decrement task

    Homework Statement The contour consists of a condenser with capacitance C = 2.22*10^-9 F and a coil of copper wire. The diameter of the wire 5*10^-4 m, the length of the coil 20*10^-2 m. Determine the damping logarithmic decrement Λ of the fluctuations? Given answer:0.018 Homework Equations...
  15. Z

    Solving Critical Damping Circuit: Find R, i, di/dt, v_C(t)

    Homework Statement In the circuit in the following figure, the resistor is adjusted for critical damping. The initial capacitor voltage is 15 V, and the initial inductor current is 6 mA. Find the numerical value of R. Find the numerical values of i immediately after the switch is closed...
  16. F

    Calculating Damping Coefficient of a Generator

    Hey, I understand that damper windings are used to stabilize the speed of the rotor under varying loads. The rotor speed is decreased or increased by the induction principle. Physically the damped windings are some sort of copper bars inserted into the pole faces of a rotor and all...
  17. W

    Damping Force in a piston: Ideal Gas versus a Fluid

    I was in my physics of the human body class and we got on the topic of pistons. It was given to me that the dampening force pertaining to such a piston filled with a gas is proportional to the square of the velocity of the piston; however, for fluids it was given as simply proportional to the...
  18. jegues

    Nyquist plot, damping factor and phase margin

    Homework Statement A Nyquist (polar) plot of a standard second-order system is shown below (drawn to scale). Suppose a unit-step function is applied as the input to this system. Determine the peak percentage overshoot expected in the system output. Homework Equations The Attempt at a...
  19. D

    Calculation of range for signal with damping

    Homework Statement Given the transmitting power of 0.1 mW and received noise of -100 dBm. Consider a signal which needs a SNR of 30 dB. Calculate the range for a signal of 0.5 MHz given that the damping for the signal is calculated as: L = 10 +8.0*f [dB/km] where f is the...
  20. 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...
  21. B

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  22. G

    Damping conditions for multi degrees of freedom

    I know that d^2<4mk for underdamped, d^2>4mk for overdamped and d^2=4mk for critically damped. This is true if there is only 1 mass and spring and damper. How to use these equations if I have 2 mass, 3 spring and 3 dampers. That is d,m,k are in 2x2 matrices. Please some one help me with this.
  23. 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...
  24. L

    Simple Harmonic Oscillator and Damping

    Homework Statement After four cycles the amplitude of a damped harmonic oscillator has dropped to 1/e of it's initial value. Find the ratio of the frequency of this oscillator to that of it's natural frequency (undamped value) Homework Equations x'' +(√k/m) = 0 x'' = d/dt(dx/dt)...
  25. R

    Determining the damping constant from the ratio of amplitudes

    Homework Statement I have measured the amplitude between the first and tenth oscillations for a damped harmonic oscillator (spring with a mass attached). I also have measured the period. First question. Is an (underdamped) harmonic oscillator periodic? Like I know that the solution to the...
  26. C

    Eddy current damping - Analysis?

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  27. R

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  28. F

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  29. C

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  30. H

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  31. C

    Knowing Damping and Spring Constant Finding Time

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  32. S

    Effect of electromagnetic damping with variable current

    Hi guys, first time poster. My question is; How would a constant damping provided by an electromagnet affect the damping ratio (and logarithmic decrement) amplitude? And how would increasing the current through the electromagnet affect the damping? So far I've found Biot-Savart's Law which...
  33. D

    Forced oscillations without damping

    Homework Statement We are to develop the equations of motion for an undamped horizontal spring system, the mass of which is being driven by a periodic force: F=F0 cos wt. I know how to do it but my teacher has defined an odd term, the meaning of which I want to be clarified. Homework...
  34. D

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    Homework Statement Hi guys, The title says it all pretty much. I need to know a handful of practical uses for each of the following, in the context of oscillatory motion (springs, pendulums etc): 1) light damping 2) critical damping 3) heavy damping Homework Equations Light...
  35. M

    Rayleigh Damping: Exploring the Dynamics of a 1D System

    Hi there, I came across the concept of Rayleigh damping. I aqm told it is unrelated to viscoelasticity and as a result is unable to reproduce the behaviour of real materials under harmonic excitation. I can not understand why. Considering for simplicity a 1D setting, a ball of mass...
  36. E

    Estimating damping factor for steel in flexural oscillation

    I am trying to estimate the damping ratio of steel in bending. I have a situation where I need to know the dynamic response of an inverted pendulum. A picture is worth a thousand words, so here you go: The vibration will be free; it is caused be the initial position of the system. I can...
  37. U

    Suspension strut design (diff eq and damping systems)

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  38. A

    Spring Differential Equation w/ Damping

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  39. V

    How Do You Calculate K for a Closed Loop Damping Ratio in Higher Order Systems?

    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...
  40. G

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  41. J

    Am I correct in saying the mass of a pendulum bob affects its damping rate

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  42. J

    Graph help on Damping effects on SHM experiment

    1. The problem Okay. So just too briefly outline my experiment: I have a pendulum bob attached to two cardboard discs, and am testing to see how the radius of the cardboard discs effects the damping of the simple harmonic oscillator (the pendulum). I have results (such as the one below which...
  43. N

    Problems with Critical Damping and Underdamping

    Homework Statement The concept of damping is new to me and the problems I have seen have had different known values than I see in the equations I have. Here's two I am working on. 1) An automobile suspension is critically damped, and its period of free oscillation with no damping is 1s...
  44. 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...
  45. Z

    Estimate Damping Coefficient of Car with Hand Bouncing & Dropping

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  46. Z

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  47. bhobba

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  48. S

    How Does Damping Affect the Dynamics of a Spring-Mass System?

    Homework Statement Spring – mass system with spring constant k = 40 N/m and mass 10 kg. a. Find the angular speed and period. Draw the response X versus time t b. Linear damping is added with ζ = 4 %. Find the angular speed and period. Draw the response c. Viscous damping is added with c1 =...
  49. T

    Work energy problem with damping?

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  50. T

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