Coupled Definition and 360 Threads

Homework Statement Solve the following coupled differential equations by finding the eigenvectors and eigenvalues of the matrix and using it to calculate the matrix exponent: $$\frac{df}{dz}=i\delta f(z)+i\kappa b(z)$$ $$\frac{db}{dz}=-i\delta b(z)-i\kappa f(z)$$ In matrix form...

Why would normal modes occur in the coupled oscillator system I.e. why the parts of system would oscillate with constant angular frequency and constant phase difference ?

Homework Statement We can treat the following coupled system of differential equations as an eigenvalue problem: ## 2 \frac{dy_1}{dt} = 2f_1 - 3y_1 + y_2 ## ## 2\frac{dy_2}{dt} = 2f_2 + y_1 -3y_2 ## ## \frac{dy_3}{dt} = f_3 - 4y_3 ## where f1, f2 and f3 is a set of time-dependent sources, and...

Hi all, I'm currently working on my bachelor's thesis in mechanical engineering. I must simulate a brake model, which consist of 1 rotor and 1 stator. The rotor rotate around z-axis and the stator move along z-axis. When pressure is on stator placed. The stator and rotor will be pressed...

I am a senior physics and mathematics major, and this is my last semester. As a result, I am taking advanced physics lab, which feels more like a grad school experiment than an undergrad. One of the labs deals with the modal analysis of three spring-mass systems placed vertically as shown in the...

Homework Statement I am trying to follow a paper, https://arxiv.org/pdf/1410.0710v1.pdf, I want to get the results obtained in equations 5 and 6 but can't quite work out how eq 3 has been diagonalized. Homework Equations eq 3 The Attempt at a Solution As the system is driven i thought I'd...

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!

I have done an experiment changing the mass ratio of coupled pendulums. To conclude I need real world applications for the coupled pendulums. But, i cannot find it online. So, it would be really helpful is someone could give examples of this. THANKS!

Hi there. I have to solve a system of coupled ordinary differential equations. I have some initial values, but in different points of the domain. The equations are all first order. Let's suppose the system looks like this: ##\displaystyle\frac{dy_1}{dz}=y_1+y_2+0.01##...

I would like to know how to solve the coupled pendulums problem when the masses of the pendulums are different. BUT the ratio of the masses are known and all other factors are kept constant. Need to find its affect on the beating frequency, but i cannot an equation for this with different...

What could cause a laser source with fiber coupled laser diodes to have extreme loss of power? The laser diodes have a wavelength of 658nm and have an output rated at 60mW but it seems as though the optical channels actually output ranges between 58 to 70mW. During some troubleshooting I...

Homework Statement Liquid nitrogen is in a dewar connected to a vacuum pump. Initial pressure in a dewar is 1atm and saturated with gaseous nitrogen. If the vacuum pump started, it removes gas in it and the pressure in a dewar will be reduced under the saturation pressure of the liquid...

I am simulating a system, where I have a semiconductor with a charge distribution in the conduction band coupled to a metal. I want to calculate the electrostatic potential due to this charge distribution but some things are confusing me. To calculate the electrostatic potential I solve Poissons...

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...

Homework Statement Consider two masses m connected to each other and two walls by three springs with spring constant k. The left mass is subject to a driving force ## F_d\cos(2 \omega t) ## and the right to ## 2F_d\cos(2 \omega t) ## Homework Equations Writing out the coupled equations: $$...

Hello everyone! For my quantum mechanics class I have to study the problem of two quantum oscillator coupled to each other and in particular to find the eigenstates and eigenergies for a subspace of the Fock space. I know that, in general, to solve this kind of problem I have to diagonalize the...

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...

Hi PF! I have a system of 4 first order linear ODE's, call each ODE ##\psi_1,...,\psi_4 : \psi = \psi(x,y,z,t)##. However, there are three algebraic variables (not ##x,y,z,t##, let's call them ##c_1,c_2,c_3##) that must be solved for as well, and I have three different (non-differential)...

Homework Statement In ##1+1##-dimensional spacetime, two objects, each with charge ##Q##, are fixed and separated by a distance ##d##. (a) A light object of mass ##m## and charge ##-q## is attached to one of the massive objects via a spring of spring constant ##k##. Quantise the motion of the...

Homework Statement Two harmonic oscillators A and B , of mass m and spring constants kA and kB are coupled together by a spring of spring constant kC .Find the normal frequencies ω' and ω'' and describe the normal modes of oscillation if (k C)2= kAkB) Homework EquationsThe Attempt at a...

According to David Tong's notes the real scalar field can't be coupled to the electromagnetic field because it doesn't have any "suitable" conserved currents. What does "suitable" mean? The real field does have conserved currents, why aren't those suitable?

One of my friends needs to numerically solve this two dimensional boundary value problem but has now idea where to begin. Could anybody help? ## [(K H )(f g_x-gf_x)]_x+[(K H )(f g_y-gf_y)]_y=0 #### K H G^2 (f^2+g^2)+\frac 1 2 [KH (f^2+g^2)_x]_x+\frac 1 2 [K H (f^2+g^2)_y]_y-K...

Homework Statement Calculate the Lagrangian of this set up: Imagine having two ropes: They are both attached to the ceiling and have different lengths. One has length b and the other has length 4b. Say they are hooked to the ceiling a distance 4b apart. Now, the ropes are both hooked to a...

Homework Statement Hi everybody! Two masses m1 and m2 are connected with a spring one after the other to a wall (see attached picture). The spring constants are k1 and k2. To consider here are only longitudinal oscillations and no external forces. a) Express the Newtonian equations of motion...

MX''=Fn(cosΦ−usinΦ) MZ''=Fn(sinΦ+ucosΦ)−Mg MΦ''=Fn(Bxx+uBz) I tried using Runge-Kutta methods to approximate motion equations in MATLAB but it turn out wrong. I also tired finding and researching forums and web for solution but to no avail. Fn,M,θ,u is constant fn/M = 0.866 it seems that i...

Greetings all, Quick question. I know that all 4 Maxwell's equations are said to be first-order, coupled PDEs, where each equation has an unknown field. I see that with Faraday's and Ampere's law, because, E and H appear in each of those equations. But Gauss' laws, I'm not seeing that...

Homework Statement Hi. I am trying to solve a problem on renormalisation group flow and have come across the following coupled equations that I need to solve: Λ ∂g/∂Λ = b.m Λ ∂m/∂Λ = -2.m + a.g Where a and b are just constants. I need to find g(Λ) and m(Λ). Homework Equations [/B] I...

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...

Good evening I have these coupled equations and was wondering if there is any chance solving them analytically. If not, how would you approach it numerically? (shown in attachment) Thank you very much

Hello, I have a problem regarding the characteristic frequencies of a coupled mass-spring system. I have made some relevant progress, but I'm unsure of where to go from here. 1. Homework Statement Find the characteristic frequencies and the two characteristic modes of vibration if the...

This is for just two separate pendulums on a string, not conjoined pendulums or ones with a spring between them. All I can think of is ∆E = mg∆h, v = √2g∆h', t = 2π√l/g' and f = 1/t.

Hello All, I have a quick question about torque and how it transfers to a coupled object. I am coupling a DC motor onto a worm gear and I need to calculate the tangential and axial forces on the worm. The Tangential Force equation is as follows: Fwt = (2*M1)/d1 where Fwt is the tangential...

I'm just wondering if all known coupled reactions are biological, or if there are some that geological and could have preceded the emergence of life on earth. In other words, are there some compounds in geochemistry that are much more abundant than you would expect if the reactions that produce...

Homework Statement The moment of the couple is 600k (N-m). What is the angle A? F = 100N located at (5,0)m and pointed in the positive x and positive y direction -F = 100N located at (0,4)m and pointed in the negative x and negative y direction Homework Equations M = rxF M = DThe Attempt at a...

Homework Statement dNa/dt = -Na/Ta where Na is the function and Ta is the constant dNb/dt = Na/Ta - Nb/Tb where Nb is the function and Tb is the constant Homework Equations My Prof said Nb(t) has the form Nb(t) = Cexp(-t/Ta) + Dexp(-t/Tb) The Attempt at a Solution I know the first equation...

Homework Statement [/B] I'm trying to 'solve' two coupled second order ODE's with the intent of putting them in state space. My specific problem is more complex and includes additional equations which are irrelevant. Essentially I can solve the problem if I know the solution to this. x1 and...

Hi, I have two coupled differential equations d^2 phi(z)/dz^2=lambda*phi(z)*(phi(z)^2+psi(z)^2-sigma^2) d^2 psi(z)/dz^2=lambda*psi(z)*(phi(z)^2+psi(z)^2-sigma^2+epsilon/lambda) where lambda, epsilon and sigma are arbitrary constants. The equation subject to the bellow boundary conditions...

Homework Statement My question is regarding part (e), I just gave all the questions for reference. Homework EquationsThe Attempt at a Solution These are the coupled equations I should solve (from part d) My issue is using ode45 to get ##C_{A}(t)##, ##C_{P}(t)##, and ##T(t)##. Here is my...

Hi, I need to solve 3 coupled first order ODE's using NDSolve (numerical solution). This is the code I have used ; NDSolve[{u'[t] == ((1 - (u[t]/t^2))/(-3 - (u[t]/t^2) - (v[t]/t^2))), v'[t] == (((u[t]/t^2) - (v[t]/t^2))/(-3 - (u[t]/t^2) - (v[t]/t^2))), w'[t] == (v[t])/(-3 t^2 - (u[t]) -...

Hi there, I have been using Leonard Susskind's lectures on classical mechanics to learn about Lagrangians and Hamiltonians, and decided to try to create a Lagrangian for the double pendulum and another pendulum-related system. I found the equations of motion, but they were unlike any...

Hello everyone, I'm struggling with a coupled of matrix equations of the general form: AX + CY = cX BY + DX = cY where A, B, C and D are hermitics square matrices. X, Y and c are the eigenvector and eigenvalue to be found. I'm looking for a method or an algorithm to solve this system by using...

I want to solve a system of 2 coupled pde (in MATLAB) of the format: c1*(df/dt)+c2*(df/dz)+c3*(f)+c4*(g)=0 (dg/dt)=c5*f+c6*g with Initial conditions as f(0,t)=1, g(z,0)=0 and f(z,0)=0 0<f,g,z,t<1 I tried using the MATLAB function pdepe to do this but got errors and if I go for numerical...

Homework Statement Consider two spins, L and R, in a magnetic field along the z-axis, i.e. B = (0, 0, B) . The magnetic moments of the two spins are coupled to each other so that the total Hamiltonian reads H = g\mu_B\mathbf{B}\cdot(\mathbf{S}_L + \mathbf{S}_R) + J \mathbf{S}_L\cdot...

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...