Damped oscillation Definition and 39 Threads

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. Y

    Functional representation of the oscillating graph

    Hi; This is in fact not a homework question, but it rather comes out of personal curiosity. If you look at the graph of the two functions in the image attached, what is the simplest functional representation for such a symmetrical pattern?
  2. VVS2000

    I Damping in a coupled pendulum system

    http://www.cts.iitkgp.ac.in/Phy_1st/Lab_WorkBook/CoupledPendula.pdf This is similar to the experiment which I did
  3. R

    Driven oscillator amplitude steady state X(t) = ##Asin(\omega t + \delta)##

    I found ## \frac{\gamma}{2} = 7##, ##\gamma = 14## ##\omega_0^2 = \omega_d^2 + \frac{\gamma^2}{4} = 25## ##\omega_0 = \omega = 25##, thus ##\delta = \frac{\pi}{2}## ##A = \frac{\frac{F_0}{m}}{\sqrt((\omega_0^2 - \omega^2)+ \gamma^2\omega^2)} = 0.04## Thus, ##X(t) = 0.04sin(25t + \frac{\pi}{3} -...
  4. R

    Calculate quality factor of a damped oscillation from a graph

    I'm trying to find the quality factor of a damped system. I know 3 points from the graph, ##(t,x): (\frac{\pi}{120},0.5), (\frac{\pi}{80},0), (\frac{\pi}{16},0)## From this I found that ##T = \frac{\pi}{20}## ##\omega_d = \frac{2\pi}{T} = 40 rad## Then, from the solution ##x(t) = A_0...
  5. vel

    Energy loss of damped oscillator

    yeah, I don't even know how to start
  6. J

    Damped Oscillation Amplitude Decrease vs. Mass Relationship

    so what I did was e^-(1/10.1)=0.9057 and e^-(1/14.8)=0.93466 Then 0.93466/0.9057 = 1.03198, so the heavier mass dampens 1.03 times more than the lighter mass. If the lighter mass decreases the oscillation to 72.1%, then the heavier mass would be 72.1%*1.03198 = 74.4, but this is wrong. It...
  7. no_drama_llama_77

    How Does a PTMD Dissipate Energy Back into the Building?

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  8. Protea Grandiceps

    I X variable in damping force equation for damped oscillation?

    Hi, for ease of reference this posting is segmented into : 1. Background 2. Focus 3. Question 1. Background: Regarding (one, linear, second-order, homogeneous, ordinary, differential) equation describing the force in a non-driven, damped oscillation: F = m.a = -k.x - b.v F =...
  9. Phantoful

    Damped harmonic oscillator for a mass hanging from a spring

    Homework Statement Homework Equations Complex number solutions z= z0eαt Energy equations and Q (Quality Factor) The Attempt at a Solution For this question, I followed my book's "general solution" for dampened harmonic motions, where z= z0eαt, and then you can solve for α and eventually...
  10. P

    Mass-spring question (frequency and amplitude)

    I am confused by this question and was hoping someone could clear this up for me, I know this is simple. A mass-spring system vibrates at 10 Hz. Ideally, i.e., without friction, it would continue forever at the same amplitude. In practice, its amplitude is found to decay such that it decreases...
  11. NihalRi

    Damped oscillation and time between displacement maximums

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  12. G

    Damped oscillation of a car on a road: velocity calculation

    Homework Statement The car circulates on a section of road whose profile can be approximated by a sinusoidal curve with the wavelength of 5.0 m. The mass of the car is 600.0 kg, and each wheel is equipped with a constant spring k = 5000 Nm-1 and a damper with constant b = 450 Nm-1s. Calculate...
  13. FallenApple

    I Galaxy Merger and Damped Oscillation?

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  14. A

    Phase problem in a damped RLC circuit

    Homework Statement The expression for electric charge on the capacitor in the series RLC circuit is as follows: q(t)=A*exp(-Rt/2L)*cos(omega*t+phi) where omega=square_root(1/LC-R^2/4L^2) What is the phase phi, if the initial conditions are: q(t=0)=Q I(t=0)=0 Homework Equations The damped...
  15. kostoglotov

    Damped vs Undamped Driven Springs and superposition?

    Modeling driven undamped spring systems in my diff eqs text at the moment. So I've just worked through the derivation of x(t) = C\cos{(\omega_0t - \alpha)} + \frac{F_0/m}{\omega_0^2-\omega^2}\cos{\omega t} And it's clear that this describes the superposition of two different oscillations...
  16. K

    A gong that makes damped oscillation

    Homework Statement A gong makes a loud noise when struck. The noise gradually gets less and less loud until it fades below the sensitivity of the human ear. The simplest model of how the gong produces the sound we hear treats the gong as a damped harmonic oscillator. The tone we hear is related...
  17. M

    Eddy currents and Torsion Pedulum

    I am having difficulties writing my damped oscillations lab report. We were asked to write a short essay on eddy currents (creation,direction advantage and disadvantage) and their relationship with torsion pendulums. Also,we have to explain if the copper wheel in the torsion pendulum could be...
  18. 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 = +_...
  19. Subhadeep Dey

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    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.
  20. S

    How do you find the center axis of a damped oscillation

    Hello! I have data of a damped oscillation (the movement on Y as it dies down in time). Imagine for example a ball that is hanging from a spring and it keeps bouncing up and down under the spring until it stops. The problem is I do not know how to find the axis around which the oscillation...
  21. Maxo

    Damped Oscillation Equation: Finding Amplitude and Phase Angle

    Homework Statement The equation for a damped oscillation is y(t)=Ae^{-\frac{b}{2m}t}cos(\omega't + \phi) We know that y(0)=0.5 and y'(0)=0. Find the values of A and ø and then plot the oscillation in MATLAB. Homework Equations See above The Attempt at a Solution When...
  22. 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...
  23. 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?
  24. 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...
  25. S

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  26. F

    How do I find the other particular solution?

    Homework Statement A Force F(t) = F0(1 - e-at), where both F0 and a are constants, acts over a damped oscillator. In t = 0, the oscillator is in it's equilibrium position. The mass of the oscillator is m, the spring constant is k = 2ma2 and the damping constant is b = 2ma. Find x(t)...
  27. A

    Newton-Raphson solution for damped oscillation

    1. The oscillation amplitude of a damped system is given by: x=-8e^0.5θ sin3θ Where θ is in radians Using the Newton-Raphson iteration method, determine the value of t, near to 5.2 correct to 4 significant figures, when the amplitude is zero. 2. Newton's equation r_2=r_1-f(r_1...
  28. W

    Damped Oscillation: Finding Time Constant

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  29. A

    How Does Damped Oscillation Apply to a Spring-Mass System on a Smooth Surface?

    Homework Statement Help need with this problem. A light spring AB of natural length 2a and of modulus of elasticity 2amn2 lies straight at its length and at rest on a smooth horizontal table. The end A is fixed to the table and a particle P of mass m is attached to the midpoint of the spring...
  30. S

    Finding angular frequency of damped oscillation

    My question is that I am asked to find the angular frequency of a spring-mass system. I am given the damping constant, the mass of the object at the end of the spring, the mass of the spring, and the spring constant. I know that angular frequency equals the square root of the spring constant...
  31. K

    Work and Power of the Friction Force in an F=-bυ damped oscillation

    Hey there forum! Consider a damped oscillation in which the friction force is F=-bυ. What I want to ask is how do you calculate the work done by this force for any x interval along a line and what is the Power of the work done by this force? I already know that Power P of the work done...
  32. A

    Why Does a System Behave as if It Has a Larger Mass in Water Compared to Air?

    Homework Statement This problem was presented as part of a lab write up. In the lab we were studying damped oscillations. We were asked to determine the mass indirectly based on values that we measured then compare it to the actual masses. We found that the calculated masses were much greater...
  33. T

    Damped Oscillation with a Driving Force (Help)

    Homework Statement A sinusoidally varying driving force is applied to a damped harmonic oscillator of force constant k and mass m. If the damping constant has a value b_1, the amplitude is A_1 when the driving angular frequency equals sqrt (k/m). In terms of A_1, what is the amplitude for...
  34. M

    Quality Factor in damped oscillation

    Working through my lecture summaries, I have been given that Q (the quality factor) =\frac{2\pi}{(\Delta E/E)cycle} and accepted this as a statement, taking \((\Delta E/E)cycle} to mean the 'energy loss per cycle'. The notes carry on to say 'The frequency \widetilde{\omega} of...
  35. R

    Damped Oscillation Homework: Calculating b & Q for Lightly Damped System

    Homework Statement A damped oscillator of mass m=1,6 kg and spring constant s=20N/m has a damped frequency of \omega' that is 99% of the undamped frequency \omega. As found out by me: The damping constant b is 0.796 kg/s. Q of the system is 7.1066 kg^-1. Are the units here right? The...
  36. B

    How Many Oscillations and Amplitude of a Damped Pendulum in 4 Hours?

    Homework Statement Given: "In a science museum, a 110 kg brass pendulum bob swings at the end of a 15.0-m-long wire. The pendulum is started at exactly 8:00 a.m. every morning by pulling it 1.5 m to the side and releasing it. Because of its compact shape and smooth surface, the pendulum's...
  37. A

    Report on Damped Oscillation: Amplitude, Applications, Comparisons

    i am going to write a report about damped oscillation . as i planned , i will discuss the amplitude decays exponentially with time , application . but that are too little to talk to then what things need to be further discuss? and one question if i use one small card and bid card to damp...
  38. 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...
  39. 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...
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