Oscillators Definition and 161 Threads

Here's what I've tried. First of all, I assume that q is positive. For particle A, then, I can write $$q E -k {\left( x _{A }-x _{B }\right) }=m \ddot{x }_{A }, $$ where ##x _{A } ## and ##x _{B } ## are the coordinates of the particles relative to their equilibrium positions from the point of...

Reference textbook “The Physics of Waves” in MIT website: https://ocw.mit.edu/courses/8-03sc-...es-fall-2016/resources/mit8_03scf16_textbook/ Chapter 2 - Section 2.3.2 [Page 47] (see attached file) Question: In the content, it states that the lifetime of the state in free oscillation is of...

Hamilton's function in this case is the sum of potential and kinetic energy? But then I don’t remember or don’t understand what to do with e. I need to find Г, but I don't understand what to do with the field.

I am wondering if it is possible to use two electromagnets oscillating at about 1 ghz to suspend an amount of ferrofluid in an acrylic chamber. As I understand it, 1 ghz should be sufficient enough to get the ferrofluid away from each magnet, as after a quick google search, magnetic fields move...

Hi, I am not sure if I have derived the matrix correctly, because of my results in task b I solved task 1 as follows, I assumed that all three particles move to the right $$m \dot{x_1}=-k(x_1 - x_2)$$ $$2m \dot{x_2}=-k(x_2-x_2)-3k(x_2-x_3)$$ $$3m \dot{x_3}=-3k(x_3-x_2)$$ Then I simply...

What is the connection between (1) Planck's quantum hypothesis that the oscillators of a blackbody can possess only discrete quantities of energy E=nhv n=1,2,3.. (2) the fact that the energy eigenvalues of the quantum harmonic oscillator wavefunction are also separated by intervals of hv...

Hi, I completely failed this homework. I mean I think I know what happen, but I don't know how to show it mathematically. The energy lost by the wave is used to oscillate the electrons inside the conductor. Thus, the electrons acts like some damped driven oscillators. I guess I have to find...

There are some articles from the 1980s where the authors discuss 1D quantum oscillators where ##V(x)## has higher than quadratic terms in it but an exact solution can still be found. One example is in this link: https://iopscience.iop.org/article/10.1088/0305-4470/14/9/001 Has anyone tried to...

Hi, I know there's are 2 normal modes because the system has 2 mass. I did the Newton's law for both mass. ##m\ddot x_1 = -\frac{mgx_1}{l} -k(x_1 - x_2)## (1) ##m\ddot x_2 = -\frac{mgx_2}{l} +k(x_1 - x_2)## (2) In the pendulum mode ##x_1 = x_2## and in the breathing mode ##x_1 = -x_2## I get...

Here is the solution I have been given: But I really don't understand this solution. Why can I just add these two exponential factors (adding two individual partition...

For an infinite system of coupled oscillators of identical mass and spring constant k. The matrix equation of motion is \ddot{X}=M^{-1}KX The eigenvectors of the solutions are those of the translation operator (since the translation operator and M^{-1}K commute). My question is, for the...

Hello, I hope the equation formatting comes out right but I'll correct it if not. So far, I have attempted to write ##\ddot{a}_k(t) = \sum_{n}(u^{k}_n)^*\ddot{q}_n(t) ##. Then I expand the right hand side with the original equation of motion, and I rewrite each coordinate according to its own...

Consider two harmonic oscillators, described by annihilation operators a and b, both initially in the vacuum state. Let us imagine that there is a coupling mechanism governed by the Hamiltonian H=P_A P_B, where P_i is the momentum operator for the oscillator i. For example P_A =...

I need to find the differential equations for each mass. ##y_1## is the equilibrium position, and ##y_2## is the second equilibrium position for each mass. I was thinking consider the next sistem: \begin{eqnarray} k\Delta y-mg&=&m\frac{d^2 y_2}{dt^2} \\ -2k\Delta y_1 -k\Delta y_2 -2mg...

Suppose we have a Hamiltonian containing a term of the form where ∂=d/dr and A(r) is a real function. I would like to study this with harmonic oscillator ladder operators. The naïve approach is to use where I have set ħ=1 so that This term is Hermitian because r and p both are.*...

Hello; I am trying to come up with an induction heater design for a machine that i am working on and am having some trouble planning it out. Anybody have some good resources? I have scoured Google and there are tons on there. I am a bit unsure how to get started. I have an induction heater...

I've tried the circuit in this article. It works very well and I've obtained 2ns clear pulses at 150 V (the main issue was to find the right avalanche voltage, which turned out to be 150-160V for my 2n3904 transistor). While the basic principles of operation in this circuit is clear for me, I...

How can I find omega on an object that is floating on water which is moving up and down on the object? The problem goes by giving you a cylindrical object with radius r and height H, pw(density of water), pc(density of circle) and x(t)=a*cos(wt). I do not understand why pw*pi*r^2*dg=pc*pi*r^2Hg

Hi, I am reading the Hajimiri-Lee phase noise model, and got a question on that. If you have an LC tank circuit that is free-running and I inject a current i(t) (dirac current) at instants either t1 or t2 (shown in the figure), depending on when you inject the phase of the output changes (as...

If we define Q factor as 2*pi* energy stored/ energy dissipated per cycle, what's the physical insight behind obtaining low phase noise for oscillators when we have high Q factors? (I know the mathematical derivation based on finding the frequency profile of an oscillator (like LC oscillator)...

If I'm given dx/dt = 2π - sin(y - x), dy/dx = 2π - sin(x - y), and finally the conditions x(0) = pi/2 and y(0) = 0, what would be the best way to hand sketch the solutions without using an explicit solution?

Homework Statement Derive the relationship bewteen x_{max}, A_{+}, A_{-} and \phi Homework Equations x(t) = e^{\gamma t}(A_{+}e^{i \omega_d t} + A_{-}e^{-i \omega_d t}) x(t) = x_{max} e^{\gamma t} cos(\omega_d t + \phi) The Attempt at a Solution I know the e^{\gamma t} cancels and for the...

In the equation 7.4, the author is taking v0=√(C/M)*x, and I don't get where does that come from. I would really appreciatte your help, thanks.

1. The problem statement Consider the case of 10 oscillators and eight quanta of energy. Determine the dominant configuration of energy for this system by identifying energy configurations and calculating the corresponding weights. What is the probability of observing the dominant...

1. The problem statementhttps://www.physicsforums.com/attachments/225935 Homework Equations3. I have rescaled coordinates which are X=(x1+x2)/√2 and Y=√3(x1-x2)/√2 for which the potential term becomes for a 2D harmonic oscillator of coordinates X and Y. But how to express Kinetic terms in terms...

Homework Statement For 300 level Statistical Mechanics, we are asked to find the partition function for a Quantum Harmonic Oscillator with energy levels E(n) = hw(n+1/2). No big deal. We are then asked to find the partition function N such oscillators. Here I am confused. Homework Equations...

1 - Is a carrier wave always made by some kind of oscillating/oscillator circuit? 2 - Does modulation "modify" or better "modulates" the carrier wave to change the audio signal to amplitude or frequency modulated? 3 - What is the difference between a "radio mixer" and "modulator" do they have...

I am studying coupled oscillations and one of the refrance I'm using says that two modes can have same frequency whereas the other one says it's impossible to have same frequency for two modes. Please help.

$$m_1 \ddot{x} - m_1 g + \frac{k(d-l)}{d}x=0$$ $$m_2 \ddot{y} - m_2 \omega^2 y + \frac{k(d-l)}{d}y=0$$ It is two masses connected by a spring. ##d=\sqrt{x^2 + y^2}## and ##l## is the length of the relaxed spring (a constant). What is the strategy to solve such a system? I tried substituting...

Homework Statement Homework EquationsThe Attempt at a Solution After the release the block will move towards right and friction will be towards the left. ##M\ddot x = f - kx## Solving for ##x##, ##x = A\cos (\omega t) + B\sin(\omega t) + f/k## Initial conditions are ##x(0) = x_0, \dot...

Are quantum harmonic oscillators, vacuum fluctuations and radiation modes the same? Is vacuum energy caused by vacuum quantum fluctuations?

Homework Statement If the amplitude of a weakly damped oscillator decreased to 1/e of its initial value after n periods, show that the frequency of the oscillator must be approximately [1 − (8π2n2)-1] times the frequency of an undamped oscillator with the same natural frequency. Homework...

Hello! I'm looking for books (or webpages, anything is welcome) with exercises dealing with methods applied to the harmonic oscillator, especially creation and annihilation operators, coherent states, squeezed states, minimum uncertainty states, Fock states, displacement operators... I have...

Homework Statement Hello! The problem is the one I attached. Homework EquationsThe Attempt at a Solution They say the answer is A, but I am not sure why. From what I remember from lab class, when you put 2 signals on x and y-axis you get usually a closed loop, like D or E. I think D happens...

Homework Statement Calculate the partition function, the entropy and the heat capacity of a system of N independent harmonic oscillators, with hamiltonian ##H = \sum_1^n(p_i^2+\omega^2q_i^2)## Homework Equations ##Z = \sum_E e^{-E/kT}## The Attempt at a Solution I am not really sure what to...

I have a system of a rod hanging on a single point, that can oscilate 360 degrees. Attached to it's lower end is a rotating disc. As you release the pendulum with a starting angle of some kind, the system oscilates. Can anyone help me analize the frequencies related to this motion? Thanks!

Homework Statement Two simple pendulums os equal length L=1m are connected with spring with a spring constant K=0,05 Mg/L. The pendulums are started by realeasing one of them from a displaced position. The subsequent motion is characterized by an oscillatory energy exchange between the...

I am trying to derive the energy spectrum of a 1D chain of identical quantum oscillators from its Hamiltonian by Fourier transforming the position and momentum operator. I came across this: https://en.wikipedia.org/wiki/Phonon#Quantum_treatment However, I am unsure of the mathematics...

I have been having trouble getting the calculation of energy for a chain of coupled oscillators to come out correctly. The program was run in Matlab and is intended to calculate the energy of a system of connected Hooke's law oscillators. Right now there is only stiffness and no dampening...

Homework Statement Consider a series of ##N## particles in a line, with the displacement of each particle from its equilibrium position labelled by ##q_{n}## and it conjugate momentum labelled by ##p_n##. Assume that the interaction between the particles is pairwise, so that the Hamiltonian is...

Homework Statement This problem is a continuation of the problem I posted in this thread: https://www.physicsforums.com/threads/equation-of-motion-from-a-lagrangian.867784/ (We have set the mass per unit length in that question to ##\sigma## = 1 to simplify some of the formulae a little.)...

I uploaded a picture of what I am stuck on. I understand the equation of motion 3.4.5a for a damped oscillator but I don't understand how to use binomial theorem to get the expanded equation 3.4.5b. I am no where near clever enough to figure this one out. I know how to use binomial theorem to...

Not a textbook/homework problem so I'm not using the format (hopefully that's ok). Can someone offer an explanation of normal modes and how to calculate the degrees of freedom in a system of coupled oscillators? From what I've seen the degrees of freedom seems to be equal to the number of...

Hey, this is more of a "share" theard, instead of a "Question" thread. I am starting my second year in a Phisics BS.c. I noticed that while poeple around me at school centinly understand HO's as well as I do, I seem to be one of the only ones who is really enjoying the subject. It is my...

I was thinking about harmonic oscillators last night when explaining the non-zero ground state energy of the quantum version to a non-scientific friend and the conversation pushed my curiosity a little so I'm wondering if anyone happens to know about any books solely about harmonic oscillators...

From my understanding of how SPI interface works, the clock basically sends out data when it is set to HIGH(or LOW). So, why does it seem like in pictures of the SPI lines, the setting of HIGH and LOW appears periodically. Can't we just put data onto DATA line, turn CLOCK line on to send, then...

I've been reading up about vacuum tubes and (more specifically) the Audion, and how they were used for instruments/amplifiers. This isn't anything I'm learning about on my degree, just things I'm reading up on myself so forgive me if I'm a little slow to grasp some parts. I understand how the...

My question concerns a really simple differential equation for the zeroth wavefunction of a harmonic oscillator. I have pretty much got it but my solution just differs by a constant,so I thought why think when one can ask other people :). Here is the equation: Where the x star represent a...

Relaxation time is defined as the time taken for mechanical energy to decay to 1/e of its original value. Why do we take a specific ratio of 1/e? What is its significance?

My question is how we describe a harmonic oscillate. Wikipedia says, "a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x." My question is, how is the harmonic oscillator a "system"? I thought...