What is Critical damping: Definition and 19 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. P

    About critical damping resistance of a ballistic galvanometer

    At critical condition, ##\omega=0## so time period will be infinite and so will be ##\lambda##.Therefore, the critical resistance will be the corresponding resistance(plus galvanometer resistance)of the asymptote of ##\lambda## vs. ##R_2## graph(the graph is a rectangular hyperbola). But here's...
  2. 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.
  3. A

    Damped Oscillatory Motion with Varying Bump Timing for Control

    First of all, the problem is not clearly defined as they don't specify if the given mass is the total mass of the car, or just the sprung mass of the car, which is really what's relevant. In any case, with the limited information given, it seems like one is forced to make the assumption that...
  4. 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...
  5. 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...
  6. dumbdumNotSmart

    Critically Damped System - Viscous force

    Homework Statement You got a plate hanging from a spring (hookes law: k) with a viscous force acting on it, -bv. If we place a mass on the plate, gravity will cause it to oscillate. Prove that if we want the plate to oscillate as little as possible (Crticial damping, no?), then $$b=2m...
  7. RJLiberator

    What Is the Value of b for Critical Damping in a Spring Balance?

    Homework Statement A spring balance consists of a pan that hangs from a spring. A damping force F_d = -bv is applied to the balance so that when an object is placed in the pan it comes to rest in the minimum time without overshoot. Determine the required value of b for an object of mass 2.5 kg...
  8. M

    Critical damping vs Overdamping

    Based on the image provided, why exactly does critical damping allow the system's amplitude to reach 0 more quickly than the case of overdamping? In overdamping, isn't the term in the NEGATIVE exponential greater in absolute value? Wouldn't this cause the system to approach 0 more rapidly? That...
  9. K

    Critical damping vs overdamping

    why critical damping and over damping doesn't undergo oscillations?
  10. 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 =...
  11. A

    DE: Critical Damping Oscillating?

    I'm having a problem understanding a critical damping model. I know critical damping is supposed to return the system to equilibrium as quickly as possible without oscillating, and a critically damped system will have repeated roots so the general solution will be: c1e^rt + c2te^rt But what...
  12. 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...
  13. 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...
  14. T

    Determine critical damping of multimass system

    Hi I have a spring mass damper system with multiple masses. Is there any way I can calculate the magnitude of the damping in order to get a critical damped system? I have the scaling of the dampers(c1/c2) and they are connected in series. c_eq=c1+c2... I tried with the formula...
  15. 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?
  16. 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...
  17. P

    Understanding Critical Damping: Exploring SHM and the T/4 Period

    Critical Damping: T/4? I read a few Textbooks on SHM. It happens to be the ones that show no mathematical derivations, that claim that Critical Damping has the period (i.e. time from 0 to equilibrium) of T/4 So I went back to my derivations of SHM considering second order differential...
  18. L

    Critical damping provides the quickest approach to zero amplitude

    Critical damping provides the quickest approach to zero amplitude for a damped oscillator. With less damping (underdamping) it approaches zero displacement faster, but oscillates around it. With more damping (overdamping), the approach to zero is slower. I got this from hyperphysics but I...
  19. E

    Prove Critical Damping: x(t)=A+Bt e^(-Beta t)

    Show that the equation x(t)=(A+Bt)e^(-Beta*t) is indeed the solution for critical damping by assuming a solution of the form x(t)=y(t)exp(-Beta*t) and determining the function y(t). Is there a differential equation for the critically damped case that I can substitute x(t) and its...