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

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    what is the equation? i have something written down in my notes but i really don't get it... x=A(e^-kt)(cos omega t) first of all, how is the amplitude calculated if it decreases over time?? is it averaged? what is e? second of all, to calculate k, you need hooke's law and you need...
  2. D

    Damped Simple Harmonic Motion problem

    I'm having trouble with this problem.The suspension system of a 2100 kg automobile "sags" 7.2 cm when the chassis is placed on it. Also, the oscillation amplitude decreases by 35% each cycle. Estimate the values of (a) the spring constant k and (b) the damping constant b for the spring and shock...
  3. F

    Damped pendulum and sliding rod

    Problem 1: I have a mathematical pendulum with a mass m connected to a string of length l. The pendulum is damped by air resistance that is proportional to the velocity, Ffric = -k*v. I need to derive the damping effect the air resistance has on the pendulum - that is, the decrease of the...
  4. F

    Damped pendulum and sliding rod

    Problem 1: I have a mathematical pendulum with a mass m connected to a string of length l. The pendulum is damped by air resistance that is proportional to the velocity, Ffric = -k*v. I need to derive the damping effect the air resistance has on the pendulum - that is, the decrease of the...
  5. D

    Damped Oscillator: Finding Work Rate & Average Power

    I am really struggling with this question...:yuck: Question: Consider a damped oscillator, with natural frequency w_0 (omega_0) and damping constant B (beta) both fixed, that is driven by a force F(t)= F_0*cos(wt). Find the rate P(t) at which F(t) does work and show that the average < P >...
  6. C

    RLC Damped Oscillator: Why Quicker to Zero in Critically Damped Case?

    Hello, On this page: http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/Oscillations.htm It says (and shows) that in the case of a critically damped oscillation, it moves more quickly to zero than in the overdamped case. I don't understand why. The solution to this circuit is...
  7. D

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    Here's the problem: A damped oscillator has a mass of .05 kg, a spring constant of 5 N/m, and a damping constant of .4 Ns/m. At t=0, the mass is moving at 3.0 m/s at x=.1m. Find x as a function of time. What I have done: I know the damping constant b = .4 and I have used this to find...
  8. B

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  9. C

    Damped and Driven Oscillation of a Bridge

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  10. E

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    Driven, damped harmonic oscillator -- need help with particular solution Consider a damped oscillator with Beta = w/4 driven by F=A1cos(wt)+A2cos(3wt). Find x(t). I know that x(t) is the solution to the system with the above drive force. I know that if an external driving force applied...
  11. R

    Damped Simple Harmonic Motion

    I'm having trouble with this problem. I want to get it into a form with cos but I'm stumped. The solution for damped simple harmonic motion is given by x = (e^(-rt/2m))(C_1*e^(iw't)+C_2*e^(-iwt)) If x = Acos phi at t = 0, find the values of C_1 and C_2 to show that x'=(approx)...
  12. S

    Navigating Damped and Forced Harmonic Motion

    hi guys, doing damped and forced harmonic motion at college at the moment, but i don't do further maths...hence I'm a tad behind compared to those who do (half the class). we don't need to know it for the exam itself, but you know...curiosity. does anyone know of any good online resources...
  13. B

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    Hi, I do not know how to drive an experession for energy loss of damped oscillator.I know that: X(t)=A exp(-Beta*t)cos(wt-delta) and: v=dx/dt... I found E=K+U but it seems to be so messy. It is like: E=(1/2)*m*(A^2)*exp(-2*beta*t)[ beta^2 (cos(wt-delta))^2)+beta* sin...
  14. A

    Overdamped and critically damped oscillator

    Can you help me start on this one: Show that an overdamped or critically damped oscillator can cross the origin at most once.
  15. E

    Lightly Damped Harmonic Oscillator

    Question: (a) Show that the total mechanical energy of a lightly damped harmonic oscillator is E = E_0 e^{-bt/m} where E_0 is the total mechanical energy at t = 0. (b) Show that the fractional energy lost per period is \frac{\Delta E}{E} = \frac{2 \pi b}{m \omega_0} = \frac{2...
  16. A

    Report on Damped Oscillation: Amplitude, Applications, Comparisons

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  17. H

    Is damped oscillation a kind of forced oscillation?

    I am confused! Forced oscillation is the one which a periodic force is imposed on a oscillating system. For a damped oscillator, the damping force is proportional to velocity which varies periodically. Does it mean that the damping force is a periodic force and the damped oscillation is a...
  18. E

    Damped Harmonic Oscillator & Mechanical Energy

    Question: A damped harmonic oscillator loses 5.0 percent of its mechanical energy per cycle. (a) By what percentage does its frequency differ from the natural frequency \omega_0 = \sqrt{k/m}? (b) After how may periods will the amplitude have decreased to 1/e of its original value? So, for...
  19. N

    Calculate b/2m for Damped Oscillations of 1.00 m Pendulum at 18.0°

    A pendulum of length 1.00 m is released from an initial angle of 18.0°. After 500 s, its amplitude is reduced by friction to 5.5°. What is the value of b/2m? i have no idea how to do this prooblem, the book goes over this section really briefly... what the heck is b/2m?
  20. W

    How to Solve a Damped Harmonic Oscillator Problem?

    Hi, I'm having a lot of trouble with a damped harmonic oscillator problem: A damped harmonic oscillator consists of a block (m=2.00kg), a spring (k=10 N/m), and a damping force (F=-bv). Initially it oscillates with an amplitude of 25.0cm. Because of the damping force, the amplitude falls...
  21. E

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  22. A

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    hello all! i'm now on a project namely "physics & sports" and I'm to study the projectile motion of a basketball. the aim of my investigation is to find out the range of projection angle theta that allows the ball to get through the "loop" (actually, what's the name of the thingy?? well i mean...
  23. G

    Damped Simple Harmonic oscillator

    a damped simple harmonic oscillator has mass m = 260 g, k = 95 N/m, and b = 75 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)? having trouble getting...
  24. M

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    I have two problems, the second of which I think I might be solving right. The web program we use to do our homework isn't accepting my answer. It might be the program's fault, but I'm not sure, so I'd like to check. Here's my first problem: Damping is negligible for a 0.131-kg object...
  25. C

    Damped Harmonic Oscillator Approximation?

    For a simple damped oscillator... \text {Apparently if } \beta \ll \omega_0 } \text { then ...} \omega_d \approx \omega_0[1-\frac {1}{2}(\beta/\omega_0)^2]} Given that: \beta=R_m/2m \text { (where } R_m= \text {mechanical resistance) } \text { and } \omega _d=\sqrt{(\omega...
  26. E

    How Does Damping Affect the Frequency and Amplitude of a Harmonic Oscillator?

    Question: A damped harmonic oscillar loses 5.0 percent of its mechanical energy per cycle. (a) By what percentage does its frequency differ from the natural frequency \omega_0 = \sqrt{k/m}? (b) After how many periods will the amplitude have decreased to 1/e of its original value? (a) Let E(t)...
  27. S

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    Hi I have two questions to ask and hopefully someone could help as I am getting little help from my college and work collegues 1) The work done by an air compressor is given by W = K [ (p1/p2)^(n-1/n) + (p1/p2)^(n-1/n)-2] where p1,p2,n and K are all constants. QUESTION - show that...
  28. C

    Damped Oscillation: Understanding Phase Difference

    In my notes, there are two sentences make me feel strange... As we know, the pendulum whose length equals to that of the friver pendulum, its natural frequency of oscillation if the same of the frequency of the driving one. This is known as resonance oscillation. However, somewhere I found...
  29. S

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    I am trying to calculate the force and velocity of a primary and secondary suspension. I know the damping constant of the dampers and the spring constant of the springs. I see where an expression can be calculated where you input time and get x.
  30. Norman

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  31. K

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  32. T

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