Coupled Definition and 414 Threads

For this problem, Would it not make sense to use for ##x' = -sx - gx - ry## as a better version of ##x' = - gx - ry## since the ##sx## term connects the two DEs to form a coupled system (from what the author explains the ##sx## term represent insulin glucose transformation). Thanks!

This exercise comes from Kleppner and Kolenkow, 2nd ed., problem 6-3. I'm using a solution key as a study reference, but the solution key is coming to a pretty different conclusion. Mostly the issue is in the equations of motion for this system. I'm not sure if there's something I'm...

Same instruction was given while finding value of 'g' by a bar pendulum. In the former case,does the spring obeys hooke's law while it forms a coupled harmonic oscillator system?Does the bar pendulum somehow breaks the simple harmonic motion(such that we can't apply the law for sumple harmonic...

Observational evidence for cosmological coupling of black holes and its implications for an astrophysical source of dark energy Comments?

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...

How should I proceed?

edit: Hello everyone! When I posted the question, latex equations that were visible in "preview" do not seem here. So, I upload a pdf version of the question. We consider zero free charges and currents: ρ=J=0 $$ \mathbf{\nabla} \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}...

Hello, In the Wikipedia article on "Inflaton" there appears the following formula: ##S=\int d^{4}x \sqrt{-g}[ \frac{1}{2}m^2_{P}R-\frac{1}{2}\partial^\mu\Phi\partial_{ \mu }\Phi-V(\Phi)-\frac{ 1 }{ 2}\xi R \Phi^]## with ##\xi## representing the strength of the interaction between R and...

A Ion source is a device that allows creating ion beams (e.g. argon ions) and to project them outside the device, for example to be further processed by a particle accelerator, or to irradiate materials or biological tissues etc. Now, suppose the ion beam is coupled with an EM wave, especially...

Hey all, I am currently struggling decoupling (or just solving) a system of coupled ODEs. The general form I wish to solve is: a'(x)=f(x)a(x)+i*g(x)b(x) b'(x)=i*h(x)a(x)+j(x)a(x) where the ' indicates a derivative with respect to x, i is just the imaginary i, and f(x), g(x), h(x), and j(x) are...

I need to use hermiticity and electromagnetic gauge invariance to determine the constraints on the constants. Through hermiticity, i found that the coefficients need to be real. However, I am not sure how gauge invariance would come into the picture to give further contraints. I think the...

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

I am a research student of MS PHYSICS. I have to numerically solve Friedman equation coupled to scalar field(phi). It is given in research paper of Sean Carroll, Mark Trodden and Hoffman entitled as ""can the dark energy equation of state parameter w be less than-1?""...

Hi, First of all, I'm not sure at all how to start this question. I found the eigenvectors in a previous question, but I'm not sure if I need it to solve this one. I think I need to use the expression for the position and velocity. ##a_n = C_n cos (\omega_n t + \alpha_n)## ##v_n = -\omega_n...

I am new to EMI modeling and just looking into it. I would like to create a circuit schematic to represent the inductive and capacitive coupling paths in one schematic. All that I've been able to find online is references discussing each independently. Is this the best approach if you want to...

Hi, I have to find the eigenvalues and eigenvectors for a system of 3 masses and 4 springs. At the end I don't get the right eigenvalues, but honestly I don't know why. Everything seems fine for me. I spent the day to look where is my error, but I really don't know. ##m_a = m_b = m_c## I got...

The equation is as attached where, - α, β and γ are constants - i1 and i2 are the variables. Also attached, is my attempt and where I stuck at. If anyone has an idea how to convert this into Bernoulli’s form, please I really need help. If there are any other ideas please let me know too...

Entangled photons are generated, for example, by parametric down conversion (SPDC). The ordinary photon beam has polarization 0° and the extraordinary photon beam comes with the polarization 90°. Each photon leaves the source in a cone of light. Both cone shells intersect in two beams, which are...

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...

So the textbook uses 3 equations for these, d 2/dt2 (y1 + y3 − √ 2y2) = − k / m (2 + 1/ √ 2 ) (y1 + y3 − √ 2y2) d 2 /dt2 (y1 + y3 + √ 2y2) = − k / m (2 − 1/ √ 2 ) (y1 + y3 + √ 2y2) d 2/ dt2 (y1 − y3) = − 2k / m (y1 − y3) Now the question is asking for the largest natural frequency. Now I...

It is the first time that I am faced with a complex field, I would not want to be wrong about how to solve this type of problem. Usually to solve the equations of motion I apply the Euler Lagrange equations. $$\partial_\mu\frac{\partial L}{\partial \phi/_\mu}-\frac{\partial L}{\partial \phi}=0$$...

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...

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...

Suppose, there is an electro-optical modulator that can couple the neighboring modes in an optical ring resonator. The Hamiltonian for the system looks something like this^^ (see the attached image). Here we sum over all modes m and 𝜙0 is a parameter. What will be a good set of basis for the...

Hi! I am looking into a mechanical problem which reduces to the set of PDE's below. I would be very happy if you could help me with it. I have the following set of second order PDE's that I want to solve. I want to solve for the generic solutions of the functions u(x,y) and v(x,y). A, B and C...

This is one of very few in-depth sources of information I can find online about Highly Coupled Magnetic Resonance...

I am not sure if i get the question... At first i would say it is impossible to give a answer, we can not distinguish. But i think if we know the phases in this instant, we can give and answer, so my answer would be: "If we know, by some reason, what are the phase in this instant, we can give...

Dear all, While simulating a coupled harmonic oscillator system, I encountered some puzzling results which I haven't been able to resolve. I was wondering if there is bug in my simulation or if I am interpreting results incorrectly. 1) In first case, take a simple harmonic oscillator system...

] I am not sure how i could begin, someone can help me? In the first mode we have a spring not stretched, while in the second, is not only stretched but the balls are outing of phase by 180 ° too.

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...

How can Vce vary from 0 to 2Vcc? In class, I learned that it was due to Lenz Law working in the transformer and a voltage of Vcc being induced to reverse the change in Ic. However, I cannot picture this. Can someone please explain with a diagram of how this comes about in the transformer windings.

This is a question from an exercise I don't have the answers to. I have been trying to figure this out for a long time and don't know what to do after writing mx''¨(t)=−kx(t)+mg I figure that the frequency ω=√(k/m) since the mg term is constant and the kx term is the only term that changes. I...

I got this picture from a superconducting parametric amplifier text I was reading. (The picture is a mechanical analog of a non-degenerate parametric amplifier.) If the balls(red and blue) were oscillating at their own natural frequencies, and an external force is driven(purple), how would the...

In order to solve for ##x##, I need to re-write the equation for ##dx## so it is independent of ##y## and ##dy##. However, I am having some issues with this. Can someone give me a push in the right direction?

Homework Statement: An adiabatic pendulum (right) is coupled via a spring with spring contant κ to a normal non-variable pendulum. The pendula have equal mass m and, initially, equal length l . The right pendulum is adiabatically pulled up with frequency ω(t) 1. Derive the equations of motion...

Hello, I’m not a physicist or studying physics in school; I’ve just read some books and have some questions that I was hoping someone could help with. Sorry if they’re a little basic. I’m trying to understand how tightly coupled matter is to spacetime. In other words, if you could look at a...

I think I know the answer,but just to make sure. I have two coupled inductors through a core that provides better flux permeability, aka a transformer, I provide say 5v and 1000 amps AC to the primary loop, in my secondary loop I have a capacitor in series with the loop (of sufficient...

Hi, So I have this question to solve and I have no idea how to do it. It states: ''How are the maximum displacements of each pendulum related for ω1 and ω2? Draw a sketch that describes the motion of the system in each case. '' The 2 angular frequencies that I have found are ω1 =√(g/l) and...

I am reading Carroll’s Spacetime and Geometry, and I have seen the word “coupled” used multiple times in seemingly different ways. I have gotten the sense that it means some sort of interaction between particles, but Carroll refers to coupling between matter fields and the curvature of...

Homework Statement The equation of motions of a series of pendulums coupled by a torsion spring is this: ##\ddot{\Phi_i}=-\frac{k}{ml^2}(2\Phi_i-\Phi_{i-1}-\Phi_{i+1})##, where k is the torsion spring constant, m is the mass of a single pendulum, and l is the length of a single pendulum. We...

Homework Statement My problem/task is to explain in elementary terms the dynamics of a string coupled pendulum, the same as in this diagram: Is it simple to make a free body diagram for the pendulums? Is it possible to understand the motion as being caused by SHM oscillation of the top...

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 Homework Equations Kirchhoff's lawsThe Attempt at a Solution Applying KVL on primary, di1/dt+i1=5+2di2/dt...1) Similarly for secondary, 2di1/dt= 4di2/dt + i2...2) After solving these equations using Laplace Transform, I got I1= 5-e-0.2t A and I2 = 2e-0.2t-2e-0.25t. I...

I have been experimenting with solenoids used to excite steel guitar strings electromagnetically. These can be found in a variety of infinite "sustainer" products such as the ebow. They generally consist of a pickup, an amplifier and a solenoid which form a simple electromagnetic feedback loop...

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 Attached Homework Equations Below The Attempt at a Solution To be honest I was going to differentiate one equation to get a 2nd order ODE and plug in the other equation, since to me ##v(0)=0## is not strong enough to do as below, am I completely mis-interpreted...

I'm working on a project at university to calculate the magnetocaloric effect of dysprosium. This will be done using a new technique designed at the university of which its not necessary to go into detail about. In short, the Dy is placed in a solenoid, through which a current runs, the current...

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.

Hello everyone (and sorry for my average english), I have to make a report on an energy harvesting system from vibrations with piezoelectric elements. During my research, i always read that there two cases in a piezoelectric harvesting system which are : weakly coupled strucutre and strongly...

Homework Statement I'm trying to solve problem a problem of complete energy of doubled pendulum (2 mathematical pendulums connected by a string). For a kinetic energy I would get (1/2) J(w_1)ˆ2 + (1/2) J(w_2)ˆ2 and for a potential energy of a spring (1/2) k (ϕ_1-ϕ_1) What about gravitational...