What is Damped oscillation: Definition and 39 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.
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?
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...
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...
"What is a tuned mass damper" by practical engineering
From 6:36 to 7:07How does the energy of the pendulum tuned mass damper (PTMD) dissipate energy back into the building? Intuitively, it seems like it's momentum or resonance, where the PTMD is in phase with the motion of the building and thus...
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 =...
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...
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...
Homework Statement
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Question 3.9
Homework Equations
equation for dampened ocillation[/B]
The Attempt at a Solution
In case this might appear confusing, I derived(with respect to t) the equation for dampened oscillation given above and tried to solve for when it equaled zero expecting...
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...
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...
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...
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...
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...
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...
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 = +_...
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.
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...
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...
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...
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...
Firstly, I spoke to a Physics teacher and some strangers on the internet as well as Googled and this is the situation I am in now. I want to build a software simulation for school of a damped-oscillation non-zero charged metallic-sphere pendulum within the uniform electric field of a...
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)...
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...
Homework Statement
The amplitude of an oscillator decreases to 36.8% of its initial value in 10.0 s. What is the value of the time constant?
Homework Equations
xmax=Ae^-bt/2m
Time constant= m/b
xmax(t)= Ae^-t/2(timeconstant)
The Attempt at a Solution
I'm not quite sure where to...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...