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

    MHB Fourier series damped driven oscillator ODE

    $$ -\sum_{n = 0}^{\infty}n^2\omega^2C_ne^{in\omega t} + 2\beta\sum_{n = 0}^{\infty}in\omega C_ne^{in\omega t} + \omega_0^2\sum_{n = 0}^{\infty}C_ne^{in\omega t} = \sum_{n = 0}^{\infty}f_ne^{in\omega t} $$ How can I justify removing the summations and solving for $C_n$? $$...
  2. S

    Damped harmonic oscillator, no clue

    Homework Statement I have a ball of 20 kg describing a damped harmonic movement, ie, m*∂^2(x)+R*∂x+K*x=0, with m=mass, R=resistance, K=spring constant. The initial position is x(0)=1, the initial velocity is v(0)=0. Knowing that v(1)=0.5, v(2)=0.3, I have to calculate K and R...
  3. C

    Equation for displacement in damped harmonic motion.

    This is not really a homework problem but rather a question about an equation for displacement in damped harmonic oscillations that I've come across during revision for midterms. In my notes and in various textbooks the equation is given as x=C\mathrm{exp}(-\frac{b}{2m}t)\cdot\mathrm{exp}(\pm...
  4. G

    Maths behind non-linear dynamics, driven damped oscillator more specifically.

    I am investigating the mathematics behind driven damped oscillators, I will then simulate it in MATLAB and observe the unpredictable long term behavior of the system. In order to create non-linearity in a oscillating spring I can no longer use hookes law but a form of it by introducing a...
  5. S

    Driven, Damped Oscillations

    Homework Statement I have a mass, B, attached to a vibrating wall. The wall is vibrating at two frequencies, .01 Hz and 75 Hz (later in the problem it turns out that we want to transmit the .01 Hz but not the 75 Hz oscillations). The spring constant is k=154 N/m, the mass of the block B is 54.7...
  6. O

    Energy of a non-linearly damped oscillator

    I was reading Strogatz's book on nonlinear dynamics and chaos and in Example 7.2.2, he stated the energy function of the nonlinear oscillator \ddot{x} + (\dot{x})^3 + x = 0 as E(x, \dot{x}) = \frac{1}{2} (x^2 + \dot{x}^2) But isn't this the energy function for the harmonic...
  7. P

    Damped Oscillator equation - Energy

    the damped oscillator equation: (m)y''(t) + (v)y'(t) +(k)y(t)=0 Show that the energy of the system given by E=(1/2)mx'² + (1/2)kx² satisfies: dE/dt = -mvx' i have gone through this several time simply differentiating the expression for E wrt and i end up with dE/dt =...
  8. P

    Damped Oscillator Equation

    the damped oscillator equation: (m)y''(t) + (v)y'(t) +(k)y(t)=0 Show that the energy of the system given by E=(1/2)mx'² + (1/2)kx² satisfies: dE/dt = -mvx' i have gone through this several time simply differentiating the expression for E wrt and i end up with dE/dt =...
  9. C

    Angular Frequency of Damped Oscillator

    1. What is the angular frequency of a damped oscillator whose spring stiffness is 15 cm with a 19.6 N mass and a damping constant of 15 kg/s? 2. ω0 = √(k/m) ----where k = spring constant and m=mass ζ= c/(2√(mk)) -----where m = mass, k = spring constant, and c = damping constant...
  10. B

    Ratio of Damped to Initial Oscillation Amplitudes - 20 Cycles

    In the figure below, a damped simple harmonic oscillator has mass m = 300 g, k = 95 N/m, and b = 70 g/s. Assume all other components have negligible mass. What is the ratio of the amplitude of the damped oscillations to the initial amplitude at the end of 20 cycles (Adamped / Ainitial)? I...
  11. D

    Solving Damped Wave Equation with Initial Conditions

    $$ u_{tt} + 3u_t = u_{xx} $$ $$ u(0,t) = u(\pi,t) = 0 $$ $$ u(x,0) = 0\quad\text{and}\quad u_t(x,0) = 10. $$ \begin{alignat*}{3} u(x,t) & = & \exp\left[-\frac{3t}{2}\right]\sin x\left[A_1\cosh\frac{t\sqrt{5}}{2} + B_1\sinh\frac{t\sqrt{5}}{2}\right]\\ & + &...
  12. D

    MHB Solution of the Damped Wave Equation under Certain Boundary Conditions

    $$ u_{tt} + 3u_t = u_{xx}\Rightarrow \varphi\psi'' + 3\varphi\psi' = \varphi''\psi. $$ $$ u(0,t) = u(\pi,t) = 0 $$ $$ u(x,0) = 0\quad\text{and}\quad u_t(x,0) = 10 $$ \[\varphi(x) = A\cos kx + B\sin kx\\\] \begin{alignat*}{3} \psi(t) & = & C\exp\left(-\frac{3t}{2}\right)\exp\left[t\frac{\sqrt{9...
  13. P

    Under damped and Over damped systems Examples

    hey, could you help me with a few examples of Underdamped and Over damped systems?
  14. D

    Forced Damped SHM, AC CLR circuit.

    Homework Statement Hello, I've recently finished an experiment on forced damped simple harmonic motion with a CLR "capacitor , inductor, resistor" circuit with the aim to measure the resonance frequency of the system, using a family of graphs for which each the resistance is varied. voltages...
  15. R

    Damped oscillator- graphical interpretation

    Hi! The damped oscillator equation is as follows: x(t)= A exp(γt/2) cos(ωt) where ω= √( (w0)^2 + (γ^2)/4 ) I have attached a graph of a damped oscillator. The question is if I use graph to measure angular frequency, will it be w0 or ω? It should be w0 because if I put γ=0, I should...
  16. C

    How Do You Calculate Energy Loss in a Damped Harmonic Oscillator?

    Homework Statement The displacement amplitude of a lightly damped oscillator with m=0.250kg and k=6400N/m is observed to decrease by 15% in exactly five minutes a) Calculate the fraction (in%0 of the initial mechanical energy of the oscillator that has been converted to other forms of energy...
  17. U

    Solution of damped oscillation D.E.

    d2x + 2Kdx + w0 2 x(t) = 0 dt dt while solving this we assume the solution to be of form x = f(t)e-kt why is this exponential taken?
  18. A

    Damped Driven Harmonic Oscillator

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  19. A

    Damped Oscillations: Does Time Change?

    Homework Statement Does the time for one oscillation, change during the damped oscillations? and please explain Homework Equations The Attempt at a Solution
  20. R

    Damped Simple Harmonic Motion: Solving for Period and Phase Delta

    Homework Statement http://img534.imageshack.us/img534/6503/questiono.jpg Homework Equations The Attempt at a Solution (a) I'm not sure how to approach this part. I appreciate any help to get me started. (b) I know that the period of oscillation is given by T'=\frac{2 \pi}{\omega '} I...
  21. jssamp

    Damped Harmonic Oscillator/ME loss/freq question

    Homework Statement A damped harmonic oscillator loses 6.0% of it's mechanical energy per cycle. (a) By what percentage does it's frequency differ from the natural frequency f_{0} = (\frac{1}{2\pi})\sqrt{\frac{k}{m}}? (b) After how many periods will the amplitude have decreased to...
  22. T

    Proportionally damped 2-DOF system

    A proportionally damped 2-DOF system has mass and stiffness matrix M and K. We also know that the system has damping ratio ζ1 = 0.1 and 2 = 0.3. The damping matrix is written as C = α M + β K + γ KM-1K Try to find the coefficients Mx"+Cx'+kx=0 CM^-1K=KM^-1C...
  23. S

    MHB Troubleshooting Damped Free Forced Vibration Solutions

    Something i am doing is not adding up. I don't understand the part with the external force. here's the question: Show that the solution for the damped free forced vibration given by is when , where something along the way I'm doing wrong, because not for heck can i get that fraction with...
  24. F

    Steady State Solution for Damped System with External Forcing

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  25. F

    What went wrong with my solution for a damped mass spring system?

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  26. E

    Increasing Damping Ratio: Does it Make a Circuit More/Less Damped?

    If the damping ratio of a damped circuit is increased, does the circuit become more or less damped? I would think it would become more damped, but what exactly is the definition of the damping ratio?
  27. J

    Amplitude from a Damped Oscillation

    Homework Statement A damped mass-spring system oscillates at 263 Hz. The time constant of the system is 7.4 s. At t = 0 the amplitude of oscillation is 3.4 cm and the energy of the oscillating system is 11 J. What is the amplitude of oscillation at t = 6.7 s? How much energy is...
  28. C

    The rate at which a damped, driven oscillator does work

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  29. teroenza

    Damped oscillator energy dissipated per cycle.

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  30. C

    Pendulum Damped by Air Resistance

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  31. M

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    Homework Statement 3. A damped oscillator's amplitude dec¡eases from 8 cm to 4 cm in 20 seconds, If the intial energy of the oscillator is 64 J, what is the energy âfter 40 seconds? (Recall: E: (l/2)kA2) Homework Equations not sure how to approach the problem The Attempt at a...
  32. S

    Driven Damped Oscillator problem

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  33. FeDeX_LaTeX

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  34. A

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  35. J

    Critically Damped Oscillator Spring Constant and Damping Parameter

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  36. L

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  37. O

    Simple Harmonic Motion/Energy: Damped Oscillations and Energy Dissipation

    Homework Statement Problem: A 2.0 kg block oscillates up and down on a spring with spring constant 240 N/m. Its initial amplitude is 15 cm. If the time constant ("tau") for damping of the oscillation is 4.0 s, how much mechanical energy has been dissipated from the block-spring system after 12...
  38. J

    Damped Oscillator and amplitude

    1. Homework Statement [/b] Consider the damped oscillator illustrated in the figure below. Assume that the mass is 365g, the spring constant is 112N/m, and b = 0.117kg/s. How long does it take for the amplitude to drop to half its initial value? (A*e-b*t/(2m))...
  39. K

    Damped mass spring system with with external forcing function

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  40. U

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  41. S

    Period doubling for a damped, driven, harmonic oscillator

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  42. N

    A Damped Oscillator and Negative Damping Force

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  43. W

    Quality factor of driven damped oscillating pendulum

    Homework Statement A small cuckoo clock has a pendulum 25 cm long with a mass of 10 g and a period of 1 s. The clock is powered by a 200 g weight which falls 2 m between the daily windings. The amplitude of the swing is 0.2 rad. What is the Q (quality factor) of the clock? How long would the...
  44. W

    Quality factor of driven damped oscillating pendulum

    Homework Statement A small cuckoo clock has a pendulum 25 cm long with a mass of 10 g and a period of 1 s. The clock is powered by a 200 g weight which falls 2 m between the daily windings. The amplitude of the swing is 0.2 rad. What is the Q (quality factor) of the clock? How long would the...
  45. E

    Steady state behavior for a particle undergoing damped forced oscillations

    Homework Statement consider a system with a damping force undergoing forced oscillations at an angular frequency ω a) what is the instantaneous kinetic energy of the system? b) what is the instantaneous potential energy of the system? c) what is the ratio of the average kinetic energy to the...
  46. F

    Damped Harmonic Oscillator -

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  47. A

    Damped Harmonic Oscillator Equation: Sum of Solutions = Another Solution?

    Hello, I am confused about how to show that any two solutions of the damped harmonic oscillator equation equal another solution. Thanks!
  48. J

    Damped Vibration, 1DOF, Worked example, Need help breaking it down.

    Homework Statement https://www.physicsforums.com/attachment.php?attachmentid=39373&stc=1&d=1317244721 Homework Equations In all honesty I am not sure? The Attempt at a Solution This question was used as a worked example in my first tutorial for Dynamics. The lecturer didn't break it down...
  49. I

    Create a graph of the position of a damped oscillator as a function of time.

    This is an assignment for a class titled "Intro to Scientific Programming" and it is a prerequisite for Computational Physics. Homework Statement Create a graph of the position of a damped oscillator as a function of time.Homework Equations The equation is x = A*e^((-b/2m)*t)cos(omega*t +...
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