Coupled Definition and 360 Threads

Homework Statement There are 3 masses connected by springs of the same spring constant (k). The end masses are connected to solid walls via 2 more springs. Assuming simple harmonic motion find the angular frequencies (\omega) for each of the normal modes of vibrations...Homework Equations The...

Homework Statement Use a coupled fourth order Runge-Kutta, to find the structure of white dwarf stars. I think I am applying the Runge-kutta method wrong? Variables defined in C code notes Homework Equations Equations in c code. and in attached images. The Attempt at a Solution This is...

Homework Statement I am asked to solve a coupled system of 5 ODEs. There is also a function, f, which describes the release of carbon dioxide over time. I am given the release rates at certain values of t and asked to interpolate for other values of t in the interval [1000 3000]. After...

Homework Statement I'm trying to solve the equations: \ddot{\phi} + 2\left(\frac{\cos \theta}{\sin \theta}\right) \dot{\theta}\dot{\phi} =0 and \ddot{\theta} - \sin \theta \cos \theta \dot{\phi^2} =0 for \theta(\lambda), \phi(\lambda) where the dots represent differentiation w.r.t...

Hello everybody, I have been trying to solve coupled two eigenvalue (Sturm-Liouville) problems in terms of two (eigen) functions u[x,y] and v[x,y]. I have been using Mathematica trying to solve the coupled equations analytically in their original form, but the Mathematica doesn't seem to...

Homework Statement I want to find the general solution of these two equations, \ddot{y}=\omega\dot{z} \ddot{z}=\omega\left(\frac{\mathbf{E}}{\mathbf{B}} - \dot{y}\right) Homework Equations These two equations are the result of quantitatively solving to find the trajectory of a charged...

I'm trying to solve equation in the attached pdf, which describes anistropic diffusion in 3D with an additional term to account for hydrogen bonding and unbonding of the diffusing substance to the medium. I've considered Laplace transforms, then solving in the Laplace domain, then inverting...

Homework Statement I have a large project involving Runge Kutta numerical solutions of differential equations. I understand the Runge Kutta method and I've done it before, but my problem involves taking the differential equation y''=sin(3y(t)), t>=0 and reexpressing this IVP into coupled...

I have a large project involving Runge Kutta numerical solutions of differential equations. I understand the Runge Kutta method and I've done it before, but my problem involves taking the differential equation y''=sin(3y(t)), t>=0 and reexpressing this IVP into coupled first order...

Sorry about the format, bit I have no knowledge of LateX. A,B - are real constants U=(Ux,Uy,Uz) I have a system of three coupled linear second order differential equations (di)^2(Ui) +A*Laplacian(Ui)+ B*di[Divergence(U)] Note: The first term is not a sum. 0<z<H, while x & y can...

Hi all, I want to solve equations of the form: \dot x + x + y = sin(\omega t) \dot y = \dot x - y This is not a standard type of form for Runge-Kutta or linear systems of equations because \dot y = f(\dot x, y, t) instead of \dot y = f(x, y, t). Any hints or links to place for...

Hi, this is a fairly basic part of the whole coupled oscillators area, but I don't really get it. My problem is with the equations of motion of a coupled oscillator: F_A=-kx_A -2k'x_A and m\ddot x_A = -kx_A -k(x_A-x_B) Everywhere I've read seems to take it as intuitive, but I don't see...

For this question I'm not going to introduce the particular problem I am working on, rather, I am merely wanting some explanation of a concept which I can't seem to find in any of my textbooks. I suspect the authors think it is just too obvious to bother explaining :smile:. I'm revising for a...

my question is: what is the general solution of this system of coupled diff. equations: f ''i = Cijfj C is a matrix, fj(z) are functions dependent of z.

Homework Statement Two identical undamped oscillators are coupled in such a way that the coupling force exerted on oscillator A is \alpha\frac{d^2x_a}{dt^2} and the coupling force exerted on oscillator B is \alpha\frac{d^2x_b}{dt^2} where \alpha is a coupling constant with magnitude less than...

Homework Statement I calculated T_o to be 1.27 seconds and "T_o"' to be 1.23 seconds, each representing a normal mode of oscillation. These are correct according to the text. Here is the question: what is the time interval between successive maximum possible amplitudes of one pendulum after...

Homework Statement Consider the system of coupled second-order differential equations u''-(t+1)(u')^2+2uv-u^3=\cos{t} 2v''+(\sin{t})u'v'-6u=2t+3 with initial conditions u(0)=1, u'(0)=2, v(0)=3, v'(0)=4. Use the second order Runge-Kutta method with h=0.2 and a=2/3, b=1/3, \alpha=\beta=3/2...

Homework Statement Ok basically we have two identical coupled pendula - each of length l with bobs of mass m connected by spring with spring constant k. so I've shown the eqns of motion are mx'' = -mgx/l + k(y-x) and my'' = -mgy/l - k(y-x) The question says: By looking for solutions...

I have a set of ten dependent variables x1, x2 ... x10 and an independent variable t. The differential equations are of the form d x1 /dt = f1(x1, x2... x10) d x2 /dt = f2(x1, x2... x10) ...... d x10 /dt = f10(x1, x2... x10) where f1, f2 ...f10 are non linear functions of x1...

I've got a set of coupled Ingegro-Differential equations that I've been working on for a while. Here they are: \frac{\partial b_x}{\partial t} = i x b_x + i u_x \frac{\partial b_y}{\partial t} = i x b_y + i u_y \frac{\partial b_z}{\partial t} = i x b_z + i u_z - \frac{3}{2 \omega} b_x...

\ddot{x}=\dot{z} \ddot{z}=\dot{x} there should be z with a dot above it just like the x, but there is none, and the code is correct as far as I know. Can someone help? Thanks.

Can fission be coupled to fusion he-3 or H3 ? The goal is to reduce long-lived by products of uranium fission for a given amount of energy (heat) released. Could uranium fission, releasing neutrons, be coupled to some kind of "neutron" fusion reaction such as H3 (tritium) or He-3 or lithium...

Homework Statement Suppose masses m_{1}, m_{2}, m_{3}, m_{4} are located at positions x_{1}, x_{2}, x_{3}, x_{4} in a line and connected by springs with constants k_{12}, k_{23}, k_{34} whose natural lengths of extension are l_{12}, l_{23}, l_{34}. Let f_{1}, f_{2}, f_{3}, f_{4} denote the...

Hi everyone, I'm dealing with system identification for the first time in my life and am in desperate need of help :) The system is spring-mounted and I'm analyzing the vertical and torsional displacements. However, it seems like the vertical and torsional oscillations are coupled (shouldn't...

I've been looking at a coupled harmonic oscillator, and normal modes of this: http://en.wikipedia.org/wiki/Normal_mode#Example_.E2.80.94_normal_modes_of_coupled_oscillators At the bottom of this example it says: This corresponds to the masses moving in the opposite directions, while the...

Homework Statement \dot{x}_i = \sum_{ n=1}^{\infty} a(n,i) x_n +b(n,i) y_n \dot{y}_i = \sum_{ n=1}^{\infty} c(n,i) x_n +d(n,i) y_n \forall i \in \mathbb{N} Homework Equations a,b,c and d are constants (though dependent on the constants n and i).The Attempt at a Solution I want to...

The problem is: Two damped harmonic oscillator are coupled. Both oscillators has same natural frequency \omega_0 and damping constant \beta. 1st oscillator is damped by 2nd oscillator. Damping force is proportional to velocity of 2nd oscillator. And, vice versa, 2nd oscillator is...

Hey guys. I want to design an AC coupled amplifier, to be powered by a 12V supply. The input voltage should be less than 30mV and the gain of the circuit should be 24dB. The circuit has 2 stages with the gain of the 1st transistor amplifier being used to amplify the signal going into the 2nd...

Just wondering does it matter which coupled differential equation you solve first ( i terms of time)? normally i just solve the first equation, so far all our tutorial question involved finding solutions to second order equations that have 2 distinct roots ( for the auxilliary equation)...

I have the following coupled ODE: 2x+y^2=d^2x/dt^2 2y+x^2=d^2y/dt^2 How would one solve for x(t), y(t)?

Homework Statement http://img27.imageshack.us/img27/2193/matlapassig2fig.jpg http://img132.imageshack.us/img132/7126/matlapassig2.jpg Homework Equations My impulse response is entirely different which make me believe that i have messed up my ODE. I have taken the laplace tranform to get it...

Homework Statement One mass m constrained to the x-axis, another mass m constrained to the y-axis. Each mass has a spring connecting it to the origin with elastic constant k and they are connected together by elastic constant c. I.e. we have a right-angle triangle made from the springs with...

What does it mean to say that two things are "coupled" or "not decoupled"? In a paper I'm reading, it says that "the vibrations and rotations are no longer decoupled for large angular momentum." (This is discussing a diatomic molecule.) What, exactly, does this mean?

Does anyone know of an example algorithm that solves coupled differential equations in either FORTRAN or C++?

I was reading about AdS/CFT and its possible description of superconductors. It is said that superconductors may exhibit a strong coupling behavior. In general, AdS/CFT is thought to be a good tool to study strong coupling dynamics. Now, my question is what are the properties that define a...

Why is it impossible to find ALL of einstein's equations in one place? well I suppose its irrelevant, I'd just like to know what math I have to do to define the energy-momentum tensor for a particle if I know say... its energy and momentum, or is that illegal? I'm struggling to grasp general...

Homework Statement Derive the equations of motion for three identical pendula A, B and C, of mass m and length L coupled together (A to B and B to C) with two identical springs of low spring constant k. Can't quite appreciate the forces acting on these pendula as they all should be...

moved to Advanced Physics Section seemed more relevant link to it is https://www.physicsforums.com/showthread.php?p=2169513#post2169513" Sorry for the double post in two spots if this can be removed Thanks Heeps

I'm not sure if I'm using the correct terminology, but just to be sure let me explain what I understand to be coupled DE's (or CDEs); A set of DEs with the all derivatives taken with respect to a single parameter t and each DE depending on the functions f1,f2,...,fn. If you guys would like to...

Any one know how these are coupled to the engine on F1 cars? http://www.greentechmedia.com/articles/shock-therapy-cars-to-get-electro-power-boosters-5159.html They seem to work well for overtaking.

Homework Statement I've actually uploaded the question. When solving problems with magnetically coupled inductors I like to add dependent sources so that I can keep everything straight. My question is when I add the dependent sources does there need to be a specific polarity to them. With...

Hi, Recently I'm trying to understand some explanation of RCWA, which introduces to computational analysis of diffraction grating efficiences. For explanation I use Soifer book, but cannot understand or don't agree with it. I tried to understand the derivation, not to write it straightforward...

I have a burning question, I was trying to find the solutions for a double mass coupled oscillation. So I found out the eigenvectors and then I arrived at this step \left( \begin{array}{c} \ddot{x_1} \\ \ddot{x_2} \end{array} \right)=\lambda \left( \begin{array}{c} x_1 \\ \ x_2 \end{array}...

The problem is: A mass m and a mass 2m are attached to a light string of unstretched length 3l _{0} , so as to divide it into 3 equal segments. The string is streched between rigid supports a distance 3l \textgreater 3l _{0} apart and the masses are free to oscillate longitudinally. The...

Homework Statement I am trying to solve a system of two coupled ODEs. I am interested in an analytic solution if that is possible. I know it will be messy. \frac{\partial^2 U_1}{\partial x^2}+a_1\frac{\partial U_1}{\partial x^2}+b_1 U_1 = c_1 U_2 \frac{\partial^2 U_2}{\partial...

Homework Statement If A, B are (complex) symmetric 3x3 matrices and det(xA-B) has three distinct solutions a,b and c, prove there exists P invertible such that PtAP = I the identity matrix PtBP = diag(a,b,c) the diagonal matrix with non-zero entries a,b and c Homework Equations...

Homework Statement \dot{x}= \cos(t) x_1 +\sin(t) x_2 \dot{y}= \sin(t) x_1 - \cos(t) x_2 Show that the solutions are unbounded. The Attempt at a Solution I tried to find the explicit solution (by hand) but I failed numerous times. What is the right course of action I...

Homework Statement two coupled pendulums are used at positions x,1 and x,2 Newton’s equation for the forces leads to the two equations: m,1 * (second derivative of x,1 with respect to t) = -k,1x,1 + k(x,2 - x,1) and m,2 * (second derivative of x,2 with respect to t) = -k,2x,2 - k(x,2...

I am trying to do a coupled field analysis, FLUID-Structure interaction. Wind strikes normally a panel covered by a very thin and flexible material that is polyethylene film and displacement of the film is what i need. The analysis is 2D. I create the flotran environment but when it comes to the...

I am trying to model a packed bed distillation column for a binary liquid in Python. Unfortunately, when I set up my system, I end up with a system of coupled non-linear first order ODEs with boundary conditions at opposite ends (feed conditions and exit conditions), and I do not know how to...