Resonance describes the phenomenon of increased amplitude that occurs when the frequency of a periodically applied force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillating force is applied at a resonant frequency of a dynamic system, the system will oscillate at a higher amplitude than when the same force is applied at other, non-resonant frequencies.Frequencies at which the response amplitude is a relative maximum are also known as resonant frequencies or resonance frequencies of the system. Small periodic forces that are near a resonant frequency of the system have the ability to produce large amplitude oscillations in the system due to the storage of vibrational energy.
Resonance phenomena occur with all types of vibrations or waves: there is mechanical resonance, acoustic resonance, electromagnetic resonance, nuclear magnetic resonance (NMR), electron spin resonance (ESR) and resonance of quantum wave functions. Resonant systems can be used to generate vibrations of a specific frequency (e.g., musical instruments), or pick out specific frequencies from a complex vibration containing many frequencies (e.g., filters).
The term resonance (from Latin resonantia, 'echo', from resonare, 'resound') originated from the field of acoustics, particularly the sympathetic resonance observed in musical instruments, e.g., when one string starts to vibrate and produce sound after a different one is struck.
My attempt is approaching this problem like the mass spring model. Considering the buoyancy force as spring force. By doing so, we can have the typical mass-spring equation
𝑚 (𝑑^2 𝑥)/(𝑑𝑡^2 )+Fbuoyancy = 𝐹_𝑒𝑥𝑡
Then I can assuming the displacement a will be the sinusoidal function...
The Fourier series for ##f(t)## is
$$f(t)=\frac{\pi}{2}-\frac{4}{\pi}\sum\limits_{n=1}^\infty \frac{\cos{(n\omega t)}}{n^2}\tag{3}$$
The steady-state periodic solution to the differential equation in ##x## is
$$x_p(t)=\frac{\pi}{2\omega_n^2}-\frac{4}{\pi}\sum\limits_{n=1}^\infty...
1) "Undamped system is forced at the same frequency as one of its natural frequencies."
Consider the 2nd order differential equation
$$\ddot{x}+\omega_0^2x=F_0\cos{\omega t}\tag{1}$$
which models a mass attached to a spring (attached to a wall) with spring constant ##k## and...
My clarinet teacher once showed me a trick: you can play any note and then sing a fifth above that note and it will create the illusion of sounding an octave deeper. On a different sub, I asked about this technique:
It turns out that this is called saxophone growling. And it's no coincidence...
Hi, I am confused by the two concepts. How are they related? So, my interpretation is that a standing wave can happen without resonance. Resonance happens when a standing wave passes energy to another object, making it vibrate. Is that right? But some say a standing wave is an example of resonance?
So I know about the 6 stable resonance Lewis Dot diagrams for sulfate:
As well as the unstable diagram that only has single bonds between the sulfur and oxygen atoms.But, is it possible for there to be other resonant structures with either 1 or 3 double bonds, even if they're more unstable? I...
So if we set the damping constant ##\beta=0## that is if we consider an undamped oscillator the amplitude becomes infinity! What is the physical meaning of this phenomena? As we know energy fed into the system is proportional to ##A^2##. So does this mean that an infinite amount of energy is...
TL;DR Summary: .
I need to find the location of following bodies MMR with Jupiter: 4:1, 3:1, with the help of Keplers third law.Keplers third law: , where P is the orbital period in Earth years, a= semi major axis in AU.
For Jupiter: Pj = years.
Now my question is, to find the location of...
I am currently learning about the coalescence model and femtoscopy, and am very confused about what resonances are. I read here (https://www.quantamagazine.org/how-the-physics-of-resonance-shapes-reality-20220126/?utm_source=pocket_saves) that they are, as all particles, an excitation of the...
"My teacher had mentioned that resonance would occur here due to the presence of a positive charge if benzene is attached. However, if we consider two bonds without breaking them, there will be one pi bond. So, will there be no resonance due to it?"
Hello everyone,
I am a student doing an internship at IMEC, Belgium. I am studying a fan driven by a motor. This fan-motor system goes into resonance at a control frequency of 36.2 Hz. This corresponds to 18.1 Hz impeller frequency. The operating range of this fan is 30 to 40 Hz, so we can't...
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 understand the function of the air cavity inside drums.
I've read that 'The air cavity inside the drum will have a set of resonance frequencies determined by its shape and size. This will emphasize some frequencies at the expense of others.'
Then what are the resonance...
I am experimenting with finding the resonant frequency of water in an attempt to disassociate the H2O bond without high voltage/current and using just tap water - no electrolytes, etc. I know how it works in classic electrolysis but that's not what I am attempting.
Assume that there is a...
I have found articles that show T1 and T2 values for mineral oil and I compare them to mine and there is over 50% error also I know that T1>T2 but mine numbers don't follow that scheme.
I got these tuning forks from someone.
However, I do not have the resonant box for amplification of the sound. I decided to get it made so that I can experience the fundamental frequency (and other harmonics) more clearly.
I am planning to provide this design.
In summary, the box would be...
I've calculated the relationships between the input impedance, line impedance and terminal impedance for a mismatched transmission line (parallel-wire type and of length ##l##). I'm now asked to consider the case where "the source [an oscillator] is in resonance with the line". What exactly does...
Hi everyone, I'm stuck on how to show the peak of the amplitude resonance curve is at wd = w0√(1-1/2Q^2), where Q = w0/γ. My first instinct is to take a derivative of something and set = 0, but what eqn?Help?
Homework Statement:: [...] Molecules with an extended π system such as linear polyenes and polyaromatic compounds are well described by resonance hybrids as well as by delocalized orbitals in molecular orbital theory.
Relevant Equations:: N/A
This is not a Homework question. I was reading...
Summary:: I would like to know if my answers of each resonance structure of the eight questions is correct or not.
I think the Inductive effect (induction) attracts electrons and affects up to three bonds as electron attracting group.
And the Mesomeric effect affects Pi- bonds as long as there...
Hi,
I've a doubt about how to the energy is stored in a 'real' RLC parallel resonant network feeds from a sinusoidal source. Take a 'real' RLC parallel network having a resistor ##R_s## in series with the inductor ##L_s## (modeling its loss) with the capacitor C in parallel and consider it in...
Hello! I'm having trouble with getting the right result in this litle example. Consider this admittance
$$ C + Cs - w^2_{pr} CCs $$ Now to get the resonance we need to set the imaginary part of the admittance 0.I did that like this
$$0 = C + Cs - w^2_{pr} CCs $$ Now I need to get ## w^2 ##...
ion shown:
My answer:
the following is the answer of the question:
I identified the major contributor correctly, but the resonance structures, but the second resonance I drew is missing in the answer sheet.
Can anyone tell me why the second resonance structure is not part of the answer...
I was told that there are six resonance structures for SO42-, as shown below.
I am wondering why this structure with single bonds is not one of the possible resonance.
I understand that it is unfavorable as the formal charges are spread out over all four atoms, but shouldn't is still be a...
This is the FM demodulation "discriminator" circuit. It is one of the simplest analog demod setups one could think of. An RF (FM) voltage signal is applied at V12 and the voltage at ' a' ' is supposed to contain the AF signal in its amplitude.
The idea behind the circuit is that it resonates at...
So, my thinking was that we use the formula
V=f(lambda)
and substitute the f so,
V = 440(lambda)
but then i don't have another number to cancel or rearrange by.
And since closed air columns have the fractions of 1/4, 3/4, and 1 1/4 (5/4), we could divide by those?
In 1D Photonic crystals, a defect can be introduced to create a defect/resonance mode and enable transmission. At first considerations, the thickness of the single defect layer determines the transmission frequency. Moreover, if it is a half-wavelength layer it will enable a resonance condition...
I can solve the equation for a damped oscillator with a forcing function.
I can then plot the Kinetic and Potential Energy.
They will be out of phase, of course (KE peaking when PE is zero, and vice versa)
And we know that when the input frequency is close to the natural frequency, the system...
Is there steric inhibition of resonance effect acting on acetate ion of acetic acid by which it breaks the equivalent resonance of COO group and destabilize the acetate ion? Please help me to understand this
Hi, can anyone provide literature that explains nuclear magnetic resonance spectroscopy in terms of a quantum mechanical theory?
Could QED explain NMR in its entire phenomenon?
Apologies for the noob question.
The frequency of the human body can be calculated based on weins law as follows:
Wavelength = 0.002898/310 = 0.00000934838 m
Plugging this into the equation λν = c we get
frequency = 299792458 / 0.00000934838 = 32069 Ghz
Elsewhere, I see that the resonant...
Hello! I am a bit confused about a resonance signal that is obtained by measuring the fluorescence signal from overlapping a laser beam with some atoms. Based on the signal shape, the maximum number of counts corresponds to the resonant frequency of the transition (ignoring for this questions...
How do we explain resonance of a complex system (say a bridge) at the atomic level? What's happening to its molecules when it's oscillating at resonance, and does that have anything to do with the frequency at which the molecules oscillate in the material?
Consider two rigid and infinitely long parallel plates (say they are of infinite length in X direction, so running from -inf to +inf in X axis) separated by a distance d (say measured in Y-direction). Let the space between the plates be filled up with a fluid that supports acoustic waves. If we...
I'm aware that the structure on the left is correct, but given that the formal charges are the same for each structure, I can't figure out why hydrogen is more likely to bond to the sulphur atom than it is to the nitrogen atom.
Thank you for your help here!
Hi All, I considered filing a patent for this invention, but instead decided to publish it so people could use it to advance the state-of-the-art in drums.
You don't need to add tape or pillows to your drum heads to muffle the overtones. Using tape or pillows also kills the strike of the...
The ##Q## factor of an oscillating system is defined as ##\omega_{r}/\Delta \omega##, where ##\omega_{r}## is the resonant frequency, and ##\Delta \omega## the resonance width. As I understand, ##Q## measures how sharp the resonance curve is.
Why is it that the resonance curve gets...
I was working on a proposal for a spacecraft , and suddenly realized that the ideal orbit may be a high inclination type of near-Earth coorbital called a "retrograde satellite" or RS orbit. Do you know of:
* A person who can compute 100 years of coorbital stability using three body (sun...
Hi all,
I would like to know what is the equation upon which I can use to determine the practical resonance frequencies in a system of second order, linear differential equations.
First some definitions: What I mean by practical resonance frequencies, is the frequencies that a second order...
Good evening.
I wanted to study the theory about Fano resonances. I tried to read the paper but it doesn't seem very pedagogical to me and I coudn't understand all the details. Are there any notes or any good book where I can find a more precise theoretical description?
Thank you
L=100mh=0.1H
ω=10^3 rad/s -> f = 159Hz
XL= ωL= 2πfL= 2π*159*0.1= 99.90 Ω
Z parallel = [(XL∠90º)*R2] / [(XL∠90º)-R2]= 37.13∠-21.8º
XC= 1/ωC= 1/(2 π f C)
I don't see how I am supposed to get to C
This might not really be that tuff a question, so the Rabi frequency...
the definition that I seem to find in multiple locations seems to be in agreement with what's on wiki here: "https://en.wikipedia.org/wiki/Rabi_frequency"
but when I am reading a book by L. Allen "optical resonance and two...
In nuclear magnetic resonance, when should one process spectra in absorption mode and when - in magnitude mode? What is benefit of using the first one and the second one? For example, I need to integrate spectrum. In this case, what should I use - absorption or magnitude mode?
I have the equation $$\frac{d^2y}{dt^2} + 5y = 0$$
where I've worked out $$y = Acos(\sqrt5t) + Bsin(\sqrt 5 t)$$
$$y'' = -5Bsin(\sqrt 5 t)
$$
using $$y = e^{\lambda x}$$ and using y(0) = 0 (the spring is released from equilibrium)
so an external force $$Acos(\omega(t - \phi))$$ is applied so...