Coupled Definition and 414 Threads

Hello, I wanted to study the behaviour of electrons in a spatially bounded system. I want to have a larger number of electrons, but I took 3 to start with and arrived at this system of coupled equations: \begin{align}\begin{bmatrix} \mathbf{\ddot{x_{1}}}\\ \\ \mathbf{\ddot{x_{2}}}\\ \\...

Hello :)I have a system which consists of two coupled ODEs for which I want to solve.F'' *(1/b²) - α²*F = Ra*(1/b³)*G G'' *(1/b²) - α*²G + Ra*(1/b²)*G = F'(1/b) In these two equations F(z) and G(z) both depend on z. b is a constant, Ra is the rayleigh number which I need to keep as Ra in my...

Can a 4th order Runge-Kutta method be used to solve an equation of this form: dVx/dt = ωVy , where ω = constant. and Vx and Vy are the x and y components of the velocity.

I understand Runga Kutta 4th order for use with a single ODE, but am not confident I have correctly derived how to apply RK4th to a coupled or 2nd order system. As example I have dy/dt=p; dp/dt=-4pi2y I recognize this as SHM with w=2pi so yes, I don't need RK to solve it, but I want to use...

Homework Statement An object A with mass 3m is suspended from a fixed point O by a spring of constant k. A second object B with mass 2m is in turn suspended from A by an identical spring. The system moves along a vertical axis through O. Find the frequencies of the normal modes, and the...

Homework Statement I have been trying to set up an LRC series circuit where in place of an inductor we have a pair of coupled coils. My aim is to determine the resonant frequency in the circuit when the voltage across the resistor or the current in the circuit is at a maximum. I am using a...

Homework Statement Hi, I already asked a question close to this, but now I have different conditions. This is the circuit C_1 = C_2 \\ R_1= R_2 The current is an AC , and I would like to know the voltage at R_1 and at R_2 I made some progress but I do not really know hot to continue...

Homework Statement Hello I want to solve the following circuit, I want to know how the voltage on R1 and R2 develop with time, It start at t=0 when there is no voltage in the circuit ( all V=0). Its a symbolic question, I need to show the equation. V1(t) = ? , V2(t) = ? The current is a DC...

Homework Statement Imagine two masses connected to each other by a string. One mass sits atop a table, while the other mass dangles below the table, as the string is fed through a hole in the center. The configuration looks like this...

If you really want to know where this comes from I am solving the GR equations for a rectilinearly isotropic metric. In other words, I can express the metric as d \tau ^2 = -T(x) dt^2 + X(x) dx^2 + dy^2 + dz^2. (It may be simpler to use a cylindrical coordinate system, but the equations come...

Homework Statement Note this question is from Morin 4.35. The system in the example in Section 4.5 is modified by subjecting the left mass to a driving force Fd*cos(2ωt), and the right mass to a driving force 2Fd cos(2ωt), where ω^2 = k/m. Find the particular solution for x1 and x2. Just...

Homework Statement Given the system in the image below, I need to find the equation of motions for the coupled system. The surface where the block moves is frictionless. The red line is position where the block is at equilibrium. At equilbrium x1 and x2 = 0. After finding the equation of motion...

Hello , I tried to solve this coupled ODE but with no success Does anyone know if there is an analytical solution to this equation? my problem is with the first & the second equations the term g*f is the my biggest problem i think once i have the solution for g - the solution for h is...

Hi, I'm not a bright programmer , but I have to solve the fallowing equations: ##\frac{df}{dt} = \alpha f -\beta f + \theta g - (f+h)f## ##\frac{dg}{dt} = \psi f- \phi g## ##\frac{dh}{dt} = \xi f+ \mu h -\tau h + \epsilon w- (f+h)h## ##\frac{dw}{dt} = \nu h - \chi h## Where ##f(t)## ...

Hi , can anybody make me sense of these equation on which i am striking my head for last 2 months. I am trying to understand piezoelectric effect. And in process of which i came to see so called strain based form of equations related to direct(Equation no.2) and reverse(Equation no. 1)...

Homework Statement I need to (analytically) solve a system of coupled second-order ODEs: (A) \frac{du}{dt} - fv = \Omega^2x (B) \frac{dv}{dt} + fu = \Omega^2y where u = \frac{dx}{dt} v = \frac{dy}{dt} subject to the initial conditions u(t=0) = U and v(t=0) = 0. Homework Equations --- The...

Q. In figure shown,if i1(t)=2tu(t) A,a voltage VCD =10u(t)mV is observed,then the placements of the dots and the value of mutual inductance M is what ? Sine current is entering the primary winding so i place a dot at "A",but where should put a dot in secondary winding.I do know that according...

Homework Statement In the given attachment (supply has voltage v(t) , ) we have to write mesh equations .I am not getting how to decide the polarity of voltage across inductor ?Homework EquationsThe Attempt at a Solution There's nothing much to do.. The only thing I am doubtful about is the...

can anyone help explain the mechanism of coupled equation transformation and when and how can i transform similar equations?

Homework Statement Consider the following pair of coupled first order ODEs \dot{y_{1}} = y_{2} with ##y_{1}(0) = 1## \dot{y_{2}} = -y_{1} with ##y_{2}(0) = 1## Use the Euler integration method with a step-size ##h = 1## and fill out the entries in the table below \begin{bmatrix}...

Given a system of two identical particles (let's say electrons), of (max) spin 1/2 (which means the magnetic quantum number of each of the electrons can be either 1/2 or -1/2), how can we write the operators (total angular momentum, z-component of the total angular momentum etc.) (a) in the...

Can anyone provide some literature on antennas spaced apart such that the spacing distance is much less than the wavelength? I am specifically interested in the mutually coupling behaviour as a function of small separation distances.

Suppose we have a quantum system with one degree of freedom, ##x##, and a heat bath (possibly modeled by a large amount of coupled oscillators) with many degrees of freedom, ##q_1 , q_2 , \dots , q_n##. If the system and bath are coupled by some interaction, this is a simple model of a system...

Hello everyone, I have the following coupled ODEs (r\geq 0) g^2v^2f(r)h^2(r)+\frac{6}{r}f'(r)-3f''(r)=0, r^2h''(r)-4f^2(r)h(r)=0, with boundary conditions f(\infty)=1, h(\infty)=1. The other 2 boundary conditions are arbitrary. Also v and g are constants, that could be set to a fixed value...

Dear all, I have posted a similar question in another forum and the general consensus seems to suggest that it is not possible to symbolic solve a system of coupled second order different equation with damping (dissipation) and driving forces. However, I have found in many papers and books...

Hello everyone I just want to ask if anyone could help me or at least tell me if it is possible to solve the couple equations using matlab I saw ode45 but that is for one equation only Thank uou

Trying to get my head around this one. Given that you can have a proton and an electron in a hydrogen atom for example, and they can create a singlet or triplet configuration, with spin 1 and spin 0 respectively. The total spin operator can be derived as: S^2 = (Se + Sp)^2 = Se^2 + Sp^2 +...

Homework Statement I'm supposed to determine the equation of motion of the two masses on the worksheet. I just need to start with that. Here is the problem statement: http://www.physics.udel.edu/~jim/PHYS211_14S/Homework%20assignments/Assignment%205%20-%20coupled%20oscillations.pdf...

Hello, I'm trying to analyze a system of elastically coupled oscillators, whose masses are all the same, using Fourier expansion. So the differential equation I am looking at right now is of the form m\frac{d^2\hat{y}_k}{dt^2} + \gamma\frac{d\hat{y}_k}{dt} - \kappa\Delta^2\hat{y}_k =...

Recently I am reading the papers in the field of PT symmetry systems. What I am confused is that in these papers, authors directly write out the equations describe the dynamics of the given systems( For example, in this paper http://arxiv.org/ftp/arxiv/papers/1103/1103.3389.pdf , authors put...

How do we solve a system of coupled differential equations written below? -\frac{d^2}{dr^2}\left( \begin{array}{c} \phi_{l,bg}(r) \\ \phi_{l,c}(r) \\ \end{array} \right)+ \left( \begin{array}{cc} f(r) & \alpha_1 \\ \alpha_2 & g(r)\\ \end{array} \right).\left( \begin{array}{c}...

A bit related to my other topic but here goes: I have the set of differential equations: x1' = a-ax1-ax2 x2' = b-bx1-bx2 What is the solution to such a set? I could google systems of differential equations, but that turns up large texts on the theory. I just wonna know in a few lines...

Homework Statement The figure below shows three rotating, uniform disks that are coupled by belts. One belt runs around the rims of disks A and C. Another belt runs around a central hub on disk A and the rim of disk B. The belts move smoothly without slippage on the rims and hub. Disk A has...

Homework Statement I have to find the normal frequencies of a coupled LC circuit. However, this LC circuit is coupled by an inductor, not a capacitor. __|C|________|C|__ |...|...| ^I(1)...|...^I(2) |...|...| {L}...{L'}...{L} |...|...| |...|...| -------------------- I'm sorry, I didn't have a...

I would like to know if a a inductively coupled power transfer system also emits electromagnetiv waves. The system contains of two inductance coils one generating the magnetic field with AC, the other picking up the magnetic energy and transforms it into an AC, also. The current frequency is...

By a fortuitous mistake in copy/pasting, I happened across this system. It exhibits very chaotic behavior for some initial values and spiral-like shapes for others. (About a 70%/30% split, respectively.) x'=cosy+sint y'=sinx+cost Here's an album of it plotted from t=0 to 1000. The titles of...

I have derived these pair of coupled diff equations for U_1 (r) and U_2 (r): r^2 \dfrac{d^2 U_1 (r)}{dr^2} + r \dfrac{d U_1 (r)}{dr} + r^2 U_2(r) = 0 and r^2 \dfrac{d^2 U_2 (r)}{dr^2} + r \dfrac{d U_2 (r)}{dr} - r^2 U_1(r) = 0 Or written in matrix form (r^2 \dfrac{d^2}{dr^2} + r...

Homework Statement Given a set of two capacitively coupled RLC circuits where each has a capacitor C and they share a coupling capacitor C^{'}. I'm trying to find nice organized material that will explain the various relevant coefficients\concepts like QF, bandwidth etc. in relation to the...

Homework Statement Consider 2 pendulums with the same length L, but 2 different masses Ma and Mb. They are coupled by a spring of spring constant k which is attached to the bobs (the masses). a) find the equations of motion b) find the frequencies and configurations of the normal modes...

Hello folks, I've been trying to understand how crystals work in crystal oscillator circuits. I understand the piezoelectric effect to the following extent: If we apply an electric field to the crystal it will deform and when the field is removed, the crystal will generate an electric field...

Hello Guys. I have to solve two coupled PDE coming from a quantum physical problem, which possesses a cylindrical symmetry. They look like this \left\{-\frac{i\hbar}{2M}\left( D^2_\rho + \frac{1}{\rho}D_\rho + D^2_z - \frac{L_z^2}{\hbar^2 \rho^2} \right) + \frac{M\omega^2_\rho \rho^2}{2} +...

Homework Statement Gearbox coupled to a flywheel. The gearbox I 92% efficient and the output shaft rotates at 5 x the speed of the input. Flywheel mass is 50kg, 0.75 m radius and is to accelerate from 0 to 300 rpm in 60 seconds. Calculate Input torque and holding torque (value and...

Thanks if you take the time to read this. Homework Statement Homework Equations The Attempt at a Solution The problem I'm getting is that I'm not getting the kinetic energy diagonal when I convert to the coordinates that diagonalize the potential energy. If you scroll all the way down you...

Homework Statement (The picture is having trouble being directed so I attached it) Hey guys, I'm trying to figure out the normal modes of a pendulum with two different masses. The lengths of the strings are the same and the weight of the strings are negligible. I can easily find everything...

Hi everyone, I am mechanical engineer by profession. I need little help from you guys. I am working on a blower which is directly coupled with motor. Now I am plannig to shift it to Belt Drive. Purpose behind doing this was that we need to save power and avoid alignment issues related to...

Given \(F = A(x)u_1^{'2} + B(x)u'_1u'_2 + C(x)u_2^{'2}\). \[ \frac{\partial F}{\partial u_i} - \frac{d}{dx}\left[\frac{\partial F}{\partial u_i'}\right] = 0 \] From the E-L equations, I found \begin{align*} \frac{d}{dx}\left[2Au_1' + Bu_2'\right] &= 0\\ \frac{d}{dx}\left[2Cu_2' + Bu_1'\right] &=...

Homework Statement A transformer has 600 primary turns and 150 secondary turns. The primary and the second resistances are 0.25Ω and 0.01 Ω respectively and the corresponding reactances are 1.0Ω and 0.04Ω respectively. Detemine the equivalent: 1. resistance 2. the reactance and 3. the...

This is solving a coupled mass problem using the techniques used in QM, it's in the mathematical introduction of Shankar. This equation was obtained by using the solution for ##x(t) = x_i(0)cos(\omega _i t)## and plugging it into ##\left| x(t) \right \rangle = \left| I \right \rangle x_i...

I have found that the kinetic energy term for each mass on a coupled (by a spring) pendulum has no \dot{y} terms, as in the the masses do not move in the y direction at all. What am I missing here? I know they are connected, but in the first normal mode, both masses should move like regular...

Dear All, Recently, I have measured a series of nonlinear vibrational spectra from which I would like to extract some useful information about kinetics of the exchange process occurring in the studied system. I need to fit my experimental data to kinetic model that is a solution of coupled...