What is Damped: Definition and 382 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. D

    Viscously Damped System: Maximum Displacement Calculation

    Homework Statement A viscously damped system has a stiffness of 5000 N/m, critical damping constant of 0.2 N-s/m, and a logarithmic decrement of 2.0. If the system is given an initial velocity of 1 m/s, determine the maximum displacement. Homework EquationsThe Attempt at a Solution From the...
  2. D

    MHB Viscously damped system

    A viscously damped system has a stiffness of \(5000\) N/m, critical damping constant of \(0.2\) N-s/m, and a logarithmic decrement of \(2.0\). If the system is given an initial velocity of \(1\) m/s, determine the maximum displacement. From the question, we have that \(k = 5000\), \(\delta =...
  3. PsychonautQQ

    Understanding Angular Displacement in Weakly Damped Harmonic Oscillators

    Hey PF. This isn't a homework question and I'm hoping this is the right place to ask it, sorry if it isn't! In the case of a weakly damped harmonic oscillator driven by a sinusoidal force of the form Fe^(iwt). The form of the differential force equation of motion is then given by ma + cv +kx =...
  4. PsychonautQQ

    Damped shm successive amplitude ratio

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  5. R

    Classical Mechanics: Lightly Damped Oscillator Driven Near Resonance

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  6. nomadreid

    Damped harmonic motion with one end without weight free

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  7. PsychonautQQ

    Energy in damped harmonic motion

    Hey PF, my book either got sloppy in a derivation or I am not connecting two very obvious dots. It gives the energy of the damped harmonic oscillator as E = (1/2)mv^2 + (1/2)kx^2 then takes the derivative with respect to time to get dE/dt. then it gives the differential equation of motion...
  8. K

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  9. R

    Derivation of damped frequency

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  10. gfd43tg

    Engineering Is My Critically Damped RLC Circuit Formula Correct?

    Hello, I am working on this problem However, I am getting a 900t term that the solution is lacking. I am wondering if what I did was wrong. My formula is consistent with the formula for a series RLC circuit that is critically damped.
  11. J

    Changing equilibrium point in damped simple harmonic motion

    Hi I have a damped simple harmonic motion model and I am altering the input force along with spring constant and damping constant. I can change the damping and spring constant to allow it to oscillate for few seconds before it stops at 0. What parameters do I need to change to alter the...
  12. S

    How do you find the center axis of a damped oscillation

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  13. J

    Instantaneous response of damped simple harmonic motion

    Hi I am trying to model SHM in Simulink as shown here: http://pundit.pratt.duke.edu/wiki/Simulink/Tutorials/DiffEq I have tried using different values of spring constant and damping to get instant response to the input force. I am measuring the displacement calculated by SHM. The force changes...
  14. Maxo

    Damped Oscillation Equation: Finding Amplitude and Phase Angle

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  15. Runei

    Coupled driven and damped oscillators

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  16. C

    Damped simple harmonic motion experiment and questions?

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  17. H

    A question about damped resonant frequency

    The standard equation for the damped angular frequency of a normal damped mass-spring system is ω_{d} = \sqrt{\frac{k}{m}-\frac{b^{2}}{4m^{2}}}. Let p=\frac{b}{2m}, we have ω_{d} =\sqrt{ω_{0}^{2}-p^{2}} Now consider that damped mass-spring system being driven by a periodic force with the...
  18. M

    Average kinetic energy of a damped oscillator

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  19. G

    Damped Oscillator Conceptual Problem and Differential Equation Solution

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  20. N

    Use Matlab to plot x(t) for damped system

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  21. D

    MHB Transfer function of a damped hanging mass

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  22. applestrudle

    Forces in Damped Forced Oscillations?

    The example I'm thinking of is a mass spring system. x = Ae^(\gamma/2)t cos(wt +a) + Ccos(wt) If the steady state has been reached, the displacement due to the free oscillations will be negligible, so does that mean that the only force acting on the mass is the driving force, F0cos(wt)...
  23. S

    How do I find the frequency of oscillation for a damped harmonic oscillator?

    Homework Statement The terminal speed of a freely falling object is v_t (assume a linear form of air resistance). When the object is suspended by a spring, the spring stretches by an amount a. Find the formula of the frequency of oscillation in terms of g, v_t, and a. Homework Equations the...
  24. L

    Queries on Damped Harmonic Motion

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  25. D

    How Does Damping Frequency Influence a Harmonic Oscillator?

    Hi, in this article: http://dx.doi.org/10.1016/S0021-9991(03)00308-5 damped molecular dynamics is used as a minimization scheme. In formula No. 9 the author gives an estimator for the optimal damping frequency: Can someone explain how to find this estimate? best, derivator
  26. O

    Damped oscillator given odd initial conditions

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  27. O

    Archived Driven, Damped Oscillator; Plot x(t)/A

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  28. A

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  29. M

    Forced Damped Oscillator frequency independent quantaties

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  30. M

    Archived Analyzing Power Absorption in a Lightly Damped Harmonic Oscillator

    Homework Statement For a lightly damped harmonic oscillator and driving frequencies close to the natural frequency \omega \approx \omega_{0}, show that the power absorbed is approximately proportional to \frac{\gamma^{2}/4}{\left(\omega_{0}-\omega\right)^{2}+\gamma^{2}/4} where \gamma is...
  31. jbrussell93

    Damped Oscillator homework

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  32. J

    Critically Damped Bathroom Scale

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  33. E

    Damped Oscillations in an RLC circuit

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  34. R

    Correlation function of damped harmonic oscillator

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  35. AJKing

    Amplitude of a Damped, Driven Pendulum

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  36. H

    Find the time constant of a damped system

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  37. A

    Damped Electromagnetic Oscillations

    Homework Statement This problem was given in my physics test, and my physics teacher was unable to provide me with an answer for it. Given a circuit made up of a generator of variable frequency, i=Im(sin2∏ft-∅) and voltage u=Um(sin2∏ft), capacitor of capacitance 1μF, resistor of resistance...
  38. F

    Graphical analysis of a damped harmonic system

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  39. B

    Short Change Resonance of a Damped, driven oscillator

    Homework Statement If both k of the spring and m are doubled while the damping constant b and driving force magnitude F0 are kept unchanged, what happens to the curve, which shows average power P(ω)? Does the curve: a) The curve becomes narrower (smaller ω) at the same frequency; b) The curve...
  40. I

    Resonance in a damped triangular potential well

    I have a potential well which is an infinite wall for x<0 and a linear slope for x>0. There is damping proportional to velocity. Basically, it's a ball bouncing elastically off the ground and with air friction included. I wonder if there is some periodic driving force which will cause one...
  41. M

    Linear Algebra: Solving a system of equations for damped oscillation

    So we are given two equations: $$ \ddot{x} - \dot{x} - x = cost (t) $$ and $$ x(t) = a sin(t) + b cos(t) $$ The question asks to find a and b. How would one go about doing this? I thought maybe substituting the $$ cos(t) $$ from equation 1 into equation 2 would work but then what...
  42. E

    Damped Simple Harmonic Motion - Finding drag constant

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  43. E

    Damped Harmonic Motion - Oscillating Spring

    Homework Statement http://www.mediafire.com/view/?7045cz9au1ci7cd A mountain bike has bad shock absorbers (w0/γ = 10) that oscillate with a period of 0.5 seconds after hitting a bump. If the mass of the bike and rider is 80kg, determine the value of the spring constant k (remembering that...
  44. E

    Fractional energy loss per cycle in a heavy damped oscillator

    http://www1.gantep.edu.tr/~physics/media/kunena/attachments/382/chapter2.pdf On page 9 and 10 of the above PDF the method for deriving the fractional energy loss per cycle in a lightly damped oscillator is described. I understand and follow this derivation. What would the derivation...
  45. E

    Understanding Damped Harmonic Motion

    So my professor was discussing the case of a mass suspended from a vertical massless spring in some viscous liquid. He arrives at the equation of motion which was :x: + \frac{b}{m}x. + \frac{k}{m}x = 0 x: is the second derivative of displacement wrt time. similarly x. is the first derivative...
  46. D

    How do you solve for A in a critically damped oscillator problem?

    Homework Statement (A) A damped oscillator is described by the equation m x′′ = −b x′− kx . What is the condition for critical damping? Assume this condition is satisfied. (B) For t < 0 the mass is at rest at x = 0. The mass is set in motion by a sharp impulsive force at t = 0, so...
  47. L

    ODE application of damped motion

    Homework Statement A mass of 40 g stretches a spring 10 cm. A damping device imparts a resistance to motion numerically equal to 560 (measured in dynes/(cm/s)) times the instantaneous velocity. Find the equation of motion if the mass is released from the equilibrium position with a downward...
  48. L

    Applications of ODE; damped motion

    Homework Statement A force of 2 lb stretches a spring 1 ft. A 3.2 lb weight is attached to the spring and the system is then immersed in a medium that imparts a damping force numerically equal to 0.4 times the instantaneous velocity. Find the equation of motion if the weight is released from...
  49. R

    Damped linear oscillator: Energy losses

    Homework Statement Hello everyone. I need to demonstrate that with a damped free oscillator, which is linear, the total energy is a function of the time, and that the time derivative of the total energy is negative, without saying if the motion is underdamped, critically damped or overdamped...
  50. C

    Damped Harmonic Oscillator/Resonance

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