Coupled Definition and 414 Threads

Homework Statement x'= E - sin x + K sin (y-x) y'= E + sin y + K sin (x-y) E and K >0 Find fixed points for this system of equations Homework Equations This system is the form of coupled oscillators described in Strogatz. θ1'= ω1 + K sin (θ2-θ1) θ2'= ω2 + K sin (θ1-θ2)...

Homework Statement Solve the equations of motion ##\ddot{y}= \omega \dot{z}## and ##\ddot{z}= \omega (\frac{E}{B}-\dot{y})## Homework Equations The Attempt at a Solution Integrate the first equation to get ##\dot{y}=\omega z + c_1## and plug into equation 2: ##\ddot{z}=\omega...

Hi I am doing this completely out of self interest and it is not my homework to do this. I hope somebody can help me. Homework Statement In the book Biological Coherence and Response to External Stimuli Herbert Fröhlich wrote a chapter on Resonance Interaction. Where he considers the...

Hi, I have posted this question to "classical physics" forum, but now I think this forum might be more appropriate. I have no idea how to move the thread here, so here is a copy.. The question seems trivial, but I want to check if I miss something. Homework Statement I'm trying to...

Homework Statement Two identical undamped oscillators, A and B, each of mass m and natural (angular) frequency $\omega_0$, are coupled in such a way that the coupling force exerted on A is \alpha m (\frac{d^2 x_A}{dt^2}), and the coupling force exerted on B is \alpha m (\frac{d^2...

Odd Form Of Eigenvalue -- Coupled Masses This isn't strictly homework, since it's something I'm trying to self-teach, but it seems to fit best here. Homework Statement It's an example of applying eigenvalue methods to solve (classical) mechanical systems in an introductory text to QM...

I am trying to solve an ODE and PDE and I am having problems coming up with a method for doing so. The PDE is: k1*(dC/dt) = k2*(dC/dx) But I have an ODE that is an expression for dC/dt: dC/dt = k3*C Where k1,k2 and k3 are constants. I planned to use the method of lines to get...

Given a general solution to the fixed-end two-mass coupled harmonic oscillator(http://teacher.pas.rochester.edu/PHY235/LectureNotes/Chapter12/Chapter12.pdf), is there a set of initial conditions for position, velocity, the 3 spring constants, and 2 masses such that a transition from random phase...

Homework Statement See attached link The Attempt at a Solution I am fine up to the point where I have to express in matrix form. My method was, given the equation for the energy, to put this in matrix form and then recover the equations of motion from there (by differentiating and...

It's been a while since I've played with systems of ODEs, and I seem to have forgotten some of the tricks. As an example, I have two coupled nonlinear DE that I want to convert to a system of four 1st order nonlinear DE. But, the normal way of making variable substitutions is not working of...

Are there any textbooks on something like this, a self consistent treatment of classical electromagnetism (relavistic is fine too) where the field equations are solved alongside with the matter fields.

Hi everyone, new member zeroseven here. First, I want to say that it's great to have a forum like this! Looking forward to participating in the discussion. Anyway, I need to solve a pair of differential equations for an initial value problem, but am not sure if an analytical solution exists. I...

Does anyone know any site with a good set of notes on coupled oscillations?

Homework Statement For the attached emitter follower circuit, calculate the maximum ac power (Sinusoidal signal) delivered to an attached load. I have already calculated Rout of the circuit as 19.2Ω, and the voltage at the emitter at operating point (no input signal) as 10.7V (I know...

hello, i am deriving an equation for designing an inductor in a coupled RLC circuit. is there an equation for calculating inductor value by knowing the input and output voltages & output current of the RLC circuit ? i have tried KVL and KCL equations but in vain. please help thank you

Hi everyone, I am currently dealing with a nonlinear system of coupled equations. In fact I had performed a perturbation approach for this system which is highly nonlinear. Thanks to first step of the perturbative approach I could reach eigenvalues in the "linear case". Right now I want to...

I'm looking for the set of equations that describe an untethered rigid body about a body fixed axis in relation to a reference axis (ECI or etc.). I'm not sure what they are called. I was trying to use DCM or Quaternions to do this, but the discrete motion nature of these won't work for my...

Homework Statement Consider a light elastic string of unstretched length ##4a_o##, stretched horizontally on a smooth surface between two fixed points a distance ##4a## apart. (##a > a_o)##. Three particles of mass m are attached so as to divide the string into four equal sections. Number...

Hi, I didn't understand the exercise so I didn't do it and my teacher doesn't give the details of the solutions. If somewone can help me and explain me the steps.. it'd be great ! Three block of mass m=0.13kg are connected with three springs of constant k1 k2 k3 and Two of the normal...

Homework Statement I need to simulate a AND/NAND gate with Emitter Coupled Logic. As I'm sure that most of you know, ECL is mostly used to make OR/NOR gates, so finding out how to make a NAND/AND gate is not as easy as it sounds. Homework Equations The Attempt at a Solution I...

Homework Statement http://i.imgur.com/zmtJ64Z.jpgHomework Equations B is a column vector {{0},{0},{1}} E is a column vector {{1},{0},{0}} v(t) is also a column vector {{v_1},{v_2},{v_3}} The Attempt at a Solution I have calculated v(t) x B to get (v_2,-v_1,0) and I made a matrix, | 0 1 0|...

Hello all, I've been interested in nuclear power and how it applies to space propulsion for awhile now. I've come across a term though that I don't quite understand. What is an optically coupled reactor? In context, it says that the design "separates the power conversion system from the...

Homework Statement A system consists of two masses. The system has normal modes of frequency wa and wb. Suppose one of the masses is displaced. How long will it take for energy to be transferred to the other mass and then back to the first mass. this question is a review question for my...

While studying the derivation of the normal modes of oscillation of a liquid sphere in the paper "Nonradial oscillations of stars" by Pekeris (1938), which can be found here, on page 193 and 194 two coupled second order differential equations in two variables are merged into one fourth order...

My teacher told me plan and design about 4 labs, okay the thing is I'm not sure about the layout of P/D for physics labs. I know there has to be expected results, I'm confused I don't know what to put there. My teacher gave me a lab manual to try and guide me okay, in the book at the end...

Hi,I'd really appreciate any help on this as I've spent many many hours trying to get my head around it. I am simulating the vaporization of a droplet in hot air and I have two equations to use: m_lc_l\frac{dT_l}{dt} = \widetilde{h}A_0(T_\infty - T_l) + \dot{m}_l(h_v-h_l) \dot{m_l} = -\frac{\pi...

Hello! I am having an issue with getting any graphs on inductance or induced voltage. In the attached circuit: What I have is a 28Vac source w/ 400hz and 2 coils (R=18.6ohm each) that are connected with a common. In the model: I have a core in the center that will be able to move up...

Homework Statement \dot{ω_{1}} = λω_{2} +μ \dot{ω_{2}} = -λω_{1} Homework Equations λ and μ are real, positive constants ω_{1}(0) ≠ 0 ω_{2}(0) ≠ 0 The Attempt at a Solution I know that the general solution will be in the form ω1(t) = A sin ωt + B cos ωt + C ω2(t) = D sin...

Help me with coupled ode45 equations in MATLAB please I have no idea to turn these into MATLAB code, and here is the porblem: y(1)' = y(2) y(2)' = - (r+re)/(L+le)*y(2) - y(1)/c*(l+le) y(3)' = y(4) y(4)' = -c*y(4).^2 /m+L*y(2).^2/(2*m) where re = ro+Rpr*z+Lpr*z' le = Lo+Lpr*z the rest...

I have to derive equations of motion from Lagrangian and stumbled upon the following system of equations (constants are simplified, that information is unneeded) \begin{cases} \ddot{x}-A\dot{y}+Bx=0 \\ \ddot{y}+A\dot{x}+Dy=0 \end{cases} This is an extension of a simpler problem where B=D...

Homework Statement (Sorry, I don't know how to use latex) Solve the TDSE for a spin half nucleus in a B-field where B_z = B0, B_y= B1 cos(ωt) and B_x = B1 sin(ωt). Use vector and matrix representation. You will get coupled differential equations for a and b, look for solutions of the form a =...

I'm new, hi all. I have two coupled equations, one of which is continuity. Basically, my problem comes down to the following system: (1) u=f(v) (similarly, v=g(u). Here, u and v are the components of a vector field, ie u=u(x,y) and v=v(x,y). (2) Continuity: \nabla \cdot \textbf{u} = 0 or...

Hello everyone, I was wondering how could you determine the period of the motion of two or more coupled oscillators. For example, two oscillators have the state variable equations: x_1=A_1\cos{(\omega_1t+\phi_1)}+A_2\cos{(\omega_2t+\phi_2)}...

http://www.google.pt/imgres?q=pendulo+acoplados+resson%C3%A2ncia&um=1&hl=pt-PT&sa=X&biw=1280&bih=656&tbm=isch&tbnid=BSwiWnZmGwlLGM:&imgrefurl=http://www.oficinadaciencia.com/Produtos/Default.aspx%3Fid%3D6493&docid=n05kCljLeoXYCM&imgurl=http://www.oficinadaciencia.com/imgs/ReadImage.aspx%253FpId%2...

Coupled physical pendulums (URGENT) Imagine that you have coupled physical pendulums like this (see image below). mass is in the inferior part of the pendulum.* Now we let the right pendulum swing without initial speed = 0 with a certain amplitude. As we know, the amplitude of the right...

Someone know how to uncouple this system of pde? Δu_{1}(x) + a u_{1}(x) + b u_{2}(x) =f(x) Δu_{2}(x) + c u_{1}(x) + d u_{2}(x) =g(x) a,b,c,d are constant. I would like to find a solution in one, two, three dimension, possibily in terms of Green function...someone could help me, please?

Hi How do you determine the forces in a coupled oscillating systems? (check the attachment for coupled oscillating system) I do get the forces right but I make mistakes with the signs.

I've attached the .pdf from which I have questions. After it says "Take the square of the numerator" halfway down the page, there is an equation that lists vector components with hats and arrows at the same time, and the arrow on other vectors. Can someone help explain the difference to me...

Homework Statement Hi I have a set of five coupled ODE, and I would like to find a solution to the first variable X in the set (the rest I call Y, Z, V, W). The equations are of the form \frac{dX}{dt} = A + BY - CX This isn't homework, but something I been working with for some time. OK, so...

Hi I am trying so solve a set of coupled ODE's. I have been able to get a solution from Mathematica using NDSolve, but when I change the coefficients an error appears: "NDSolve::mxst: Maximum number of 10000 steps reached at the point t == 0.0000748339914040257`. >>" I have tried...

Hi, I have a relatively small system. It takes 10 minutes to perform a CCSDT calculation. I know scaling is notoriously bad, but does anyone have a rough idea of how long a CCSDTQ calculation would take on the same system? Are we talking days or months? Thomas

All, As part of my research I came up with a boundary value problem where I need to solve the following system of coupled PDE: 1- a1 * f,xx + a2 * f,yy + a3 * g,xx + a4 * g,yy - a5 * f - a6 * g = 0 2- b1 * f,xx + b2 * f,yy + b3 * g,xx + b4 * g,yy - b5 * f - b6 * g = 0 Where, ai's...

My question is about generalization of most simple problem in semi-classical quantum optics. Composite system of two-level systems. single system's diagram: http://ars.sciencedirect.com/content/image/1-s2.0-S0030401807009777-gr1.jpg where atomic frequency: wab=wa - wa; probing frequency...

Hello, In my study i came across to solve the analytical solution for coupled equation y(x,t) and z(x,t).The equations contains" f " function which is a function of the first variable exponentially. The first equation is : ∂y/∂t=∂^2(y)/∂x^2- 2*f(y)*z; The second equation ...

Hello every one, In my physics problem, i end up having two coupled second-order nonlinear differential equations where the coupling terms include, the variable, the first derivatives, and also a second derivative coupling. I appreciate any help on how to handle this system before setting it...

How does one go about plotting the effects of the frequency of the driving force vs the amplitude of the masses in a system such as the one pictured below? Assume that I have already figured out what my two angular frequencies are, and the amplitues under driven force (the actually equations...

I am trying to solve four coupled equations. Three of them are first order differential equations and the fourth is a algebraic one. The equations look something like this: V_{l}(r) = f_{1}(r)W'_{l}(r) (1) h''_{l} + f_{2}(r)h'_{l} + f_{3}(r)h_{l}(r) = U_{l}(r) (2) f_{4}(r)U'_{l} +...

Attached is the formula for the equation of motion for a system of coupled oscillators. Could someone please tell me what the variables and indices refer to here? Thanks! :)

Hi I would like to know if I have a system of coupled harmonic oscillators whether the standard position operator for an uncoupled oscillator is valid, i.e. x_i = \frac{1}{\sqrt{2}} (a_i+a_i^\dagger)? where i labels the ions. To give some context I am looking at a problem involving a...

Hi all, I have a system of 3 coupled linear PDEs which can be expressed in matrix form as: \left( \begin{array}{ccc} \alpha_1 \partial_{\theta} & \alpha_2 & \alpha_3 \\ \beta_1 \partial_r & \beta_2 & \beta_3 \\ 0 & \gamma_2 \partial_{\theta} & 1 + \gamma_3 \partial_r \\ \end{array}...