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. B

    Damped Oscillators: Homework Solution

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  2. hilbert2

    Insights Damped Motion in Classical and Quantum Mechanics - Comments

    hilbert2 submitted a new PF Insights post Damped Motion in Classical and Quantum Mechanics Continue reading the Original PF Insights Post.
  3. TheBigDig

    Acceleration amplitude of a damped harmonic oscillator

    Homework Statement The acceleration amplitude of a damped harmonic oscillator is given by $$A_{acc}(\omega) = \frac{QF_o}{m} \frac{\omega}{\omega _o} \sqrt{\it{R}(\omega)}$$ Show that as ##\lim_{\omega\to\infty}, A_{acc}(\omega) = \frac{F_o}{m}## Homework Equations $$\it{R}(\omega) =...
  4. 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...
  5. patrickmoloney

    Finding the Zeros of Damped Harmonic Motion Equations

    Homework Statement Solve the damped harmonic motion system \ddot{x} + 2k\dot{x} + \omega^2 x = 0 with initial conditions \dot{x}=V at x = 0 in the cases (i) \, \omega^2 = 10k^2 (ii) \omega^2 = k^2 (iii) \omega^2 = 5, k = 3 Identify the type of damping, sketch the curve of x versus t>0 in...
  6. B

    Average energy of a damped driven oscillator

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  7. D

    Theoretical model for damped harmonic oscillation.

    Homework Statement Hello all, I have a question regarding the damping constant for a model of a vertically oscillating mass on a spring. I have read through one or two similar questions on this site but I think I can manage to be a little more specific about what I'm asking. I am in a physics...
  8. Arup Biswas

    Are light waves/ EM waves damped?

    We can't see objects from objects far away from us. Why? I think light waves damps! When it reaches our eyes it's amplitude is too small to be visualised! Is this true? If indeed EM waves are damped then why? If not please give a suitable definition for the mentioned phenomena too !
  9. J

    Diagonalize a coupled damped driven oscillator

    Homework Statement I am trying to follow a paper, https://arxiv.org/pdf/1410.0710v1.pdf, I want to get the results obtained in equations 5 and 6 but can't quite work out how eq 3 has been diagonalized. Homework Equations eq 3 The Attempt at a Solution As the system is driven i thought I'd...
  10. FallenApple

    I Galaxy Merger and Damped Oscillation?

    So it is a known fact that the Andromeda galaxy will collide and merge with the Milky Way galaxy. In the video it shows the collision. Time 1:40 My question is how does it take only 3 collisions for the merger to take place? First all, can we assume that if no stars/dark matter/planets from...
  11. N

    (Hard) work done by damped, driven oscillator as function of time

    Homework Statement Force F = const is applied to H.O. initially at rest with mass m, freq w0, damping T. Find x(t). Find work as function of time. Homework Equations mx'' + Tx' + kx = F for F= Constant The Attempt at a Solution First obtain complimentary solution for free H.O. which I get...
  12. J

    What is the value of b for a damped harmonic oscillator with given parameters?

    Homework Statement A damped harmonic oscillator consists of a block (m = 2.72 kg), a spring (k = 10.3 N/m), and a damping force (F = -bv). Initially, it oscillates with an amplitude of 28.5 cm; because of the damping, the amplitude falls to 0.721 of the initial value at the completion of 7...
  13. T

    Steady State Solution of Forced, Damped Harmonic Oscillator

    Homework Statement A damped harmonic oscillator is driven by an external force of the form $$F_{ext}=F_0sin(\omega t)$$ Show that the steady state solution is given by $$x(t)=A(\omega)sin(\omega t-\phi)$$ where $$ A(\omega)=\frac{F_0/m}{[(\omega_0^2-\omega^2)^2+4\gamma^2\omega^2]^{1/2}} $$ and...
  14. D

    Ratio of the periods of a damped and undamped oscillator

    Homework Statement Given: The amplitude of a damped harmonic oscillator drops to 1/e of its initial value after n complete cycles. Show that the ratio of period of the oscillation to the period of the same oscillator with no damping is given by \frac {T_d} {T_0} = \sqrt {1+ \frac {1}...
  15. Captain1024

    Evaluate the Fourier Transform of a Damped Sinusoidal Wave

    Homework Statement Evaluate the Fourier Transform of the damped sinusoidal wave g(t)=e^{-t}sin(2\pi f_ct)u(t) where u(t) is the unit step function. Homework Equations \omega =2\pi f G(f)=\int ^{\infty}_{-\infty} g(t)e^{-j2\pi ft}dt sin(\omega _ct)=\frac{e^{j\omega _ct}-e^{-j\omega _ct}}{2j}...
  16. J

    A Free damped vibration of a system of 2 dof, demostration

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  17. J

    A Free damped vibration of a system of 2 dof, demostration

    Hi,I need help please, i want to know how to solve de differential equation of a system of two degree of freedom using Heigenvalues or Heigenvectors or if I can use any another way to solve this kind of equations.
  18. A

    Phase problem in a damped RLC circuit

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  19. A

    Lyapunov exponents of a damped, driven harmonic oscillator

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  20. JulienB

    Damped and undamped oscillations (integration?)

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  21. T

    Damped Harmonic Oscillator and Resonance

    Homework Statement On June 10, 2000, the Millennium Bridge, a new footbridge over the River Thames in London, England, was opened to the public. However, after only two days, it had to be closed to traffic for safety reasons. On the opening day, in fact, so many people were crossing it at the...
  22. J

    MHB Damped spring differental equation

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  23. T

    I Damped Oscillators and Binomial theorem step

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  24. N

    Question about free damped vibration in an SD

    Homework Statement "If a horizontal force of F = 299kN is applied to the right at the girder level by a hydraulic jack and then the force is removed suddenly, find the equation of motion of the girder. Consider 5% critical damping. Find the displacement and velocity of the girder at 0.2 seconds...
  25. Dusty912

    Damped harmonic oscillator Diff. Eq. question

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  26. RJLiberator

    Mean Input Power & Q value , Damped Harmonic Motion

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  27. E

    Damped Simple Harmonic Motion: Finding Amplitude Reduction in Carbon Dioxide

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  28. RJLiberator

    Heavily Damped Oscillator Equation

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  29. RJLiberator

    Verifying a solution to Damped SHM

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  30. kostoglotov

    Damped vs Undamped Driven Springs and superposition?

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  31. L

    Amplitude of damped mass-spring system

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  32. K

    A gong that makes damped oscillation

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  33. R

    Optimizing Damping Time: Which Application Would Benefit Most?

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  34. H

    Are all damped oscillations periodic?

    I know the equation for damped oscillation where the damping force depends on velocity. In that case the damped oscillation has a fixed angular frequency and thus time period! I am wondering if there are any types of damped oscillation where the time period is not constant i.e. the motion is not...
  35. D

    What Is the Maximum Speed of a Mass in a Driven Damped Oscillator?

    Homework Statement A small block (mass 0.25 kg) attached to a spring (force constant 16 N/m) moves in one dimension on a horizontal surface. The oscillator is subject to both viscous damping and a sinusoidal drive. By varying the period of the driving force (while keeping the drive amplitude...
  36. H

    Chaos (Non-Linear Dynamics) Driven Damped Pendulum

    I want to investigate the phenomenon of Chaos in the form of how its driving amplitude affects _____, in a driven, damped pendulum, using a computer simulation given. Initially I was looking at 'degree of chaos' for the dependent variable - to measure this I wanted to use the Lyapunov...
  37. U

    Exponentially damped dipole - line broadening

    For an EM wave close to the transition frequency ##\omega_{21}##, we assume the dipole moment to be exponentially damped and oscillating: p(t) = p(0) e^{-\frac{\gamma}{2}t} cos(\omega_0 t) Why do we expect the electric field to be proportional to ##\dot p##? Taken from my lecturer notes on...
  38. bananabandana

    Energy of a Forced, Damped Oscilator

    Homework Statement A forced damped oscilator of mass ##m## has a displacement varying with time of ##x=Asin(\omega t) ## The restive force is ## -bv##. For a driving frequency ##\omega## that is less than the natural frequency ## \omega_{0}##, sketch graphs of potential energy, kinetic energy...
  39. B

    Damped Oscillatory motion : Period

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  40. A

    Frequency of damped mass-spring system

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  41. Phynos

    Time taken for energy to drop 95% in damped SHO

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  42. V

    How many oscillations until a damped block comes to rest?

    Homework Statement A block of mass m is attached to a spring of spring constant k. It lies on a floor with coefficient of friction μ. The spring is stretched by a length a and released. Find how many oscillations it takes for the block to come to rest. Homework Equations d2x/dt2 + k/m x = +_...
  43. B

    Relaxation Time in Damped Harmonic Oscillators

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  44. V

    Damped Driven Harmonic Oscillator.

    Homework Statement An oscillator with mass 0.5 kg, stiffness 100 N/m, and mechanical resistance 1.4 kg/s is driven by a sinusoidal force of amplitude 2 N. Plot the speed amplitude and the phase angle between the displacement and speed as a function of the driving frequency and find the...
  45. B

    Inhomogeneous damped wave equation

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  46. Sneakatone

    Damped spring problem with laplace transform

    Homework Statement A 4-pound weight stretches a spring 2 feet. The weight is released from rest 15 inches above the equilibrium position, and the resulting motion takes place in a medium offering a damping force numerically equal to 7/8 times the instantaneous velocity. Use the Laplace...
  47. grandpa2390

    What is the energy loss of damped oscillator

    Homework Statement what is the energy loss of the damped oscillator. Homework Equations x(t) = A*e^(-Bt)*cos(w1*t) T = 1/2 mv^2 The Attempt at a Solution To solve for an undamped oscillator, I took the derivative of the equation of motion x(t) and plugged the amplitude into 1/2 mv^2 equation...
  48. Subhadeep Dey

    Applications of Damped Oscillation (in Vibrations): Researching for a Paper

    I've been researching on Damped Oscillation (in vibrations) for a few days for a research paper, however I couldn't find any applications. I would be very thankful if anyone can tell me about its applications.
  49. P

    Damped ocillator LCR circuit

    Homework Statement Homework EquationsThe Attempt at a Solution For part (a) i did the following; the time for it to decay to 40% is half the period of the square wave = 0.00002 seconds So, 0.4qm = qm ## e^(\frac{-0.00002R}{2L})cos(25000*2*\pi*0.00002) ## But the cosine term yields -1 which...
  50. shanepitts

    Inquiry about Damped Oscillators

    Hello, I have two quick inquiries related to my studies on analytical mechanics. The first is I don't quite fathom how a full-width-half-maximum of the resonance of a forced and damped oscillator behaves in relation to the Q-factor?? And the second is does the amplitude of a forced and...
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