Coupled Definition and 360 Threads

Ok guys, I've got an issue with a coupled differential equation and I just can't get to solve it: \frac{\partial r}{\partial t} = Q\frac{\partial c}{\partial t} Obviously, r depends on c and visa versa, but they both depend on time. Is there a way to uncouple these variables and solve the...

Hey, I've been trying to solve this question from Goldstein's Classical Mechanics. The picture I have of the question is from a later edition and the hint was removed from the question, the hint was let η3=ζ3...

Homework Statement This problem is from the 1992 GRE. A tube is free to slide on a frictionless wire. On each end of the tube is attached a pendulum. The mass of the tube is M. The length and mass of the pendula are l and m, respectively. Homework Equations It is given that one of the...

I REALLY need help with this one guys! As of right now I believe I only need help with just the set up of the problem. The rest is just solving a differential equation and I assume the frequencies they want will just pop out. Homework Statement Two identical springs and two identical...

Homework Statement |--------------------| m|----------m-------- |m |--------------------| -------> x : positive x-axis This is a picture of a coupled oscillator in equilibrium. All three masses are equal and the spring constant on the long springs are k and the two short...

I have a system of non-linear coupled PDEs, taken from a paper from the 1980s which I would like to numerically solve. I would prefer not to use a numerical Package like MatLab or Mathematica, though I will if I need to. I would like to know if anyone knows how to solve non-linear coupled...

Hi everyone Homework Statement At first I want to find the langrangian function and the equation of motion for a system which exists of 2 masses(m) coupled by a spring(k). It's moving in 3 dimensions.We shall use cylindrical coordinatesHomework Equations LangrangianThe Attempt at a Solution...

hi, when i was making a rc coupled amplifier but as soon as i connect the input signal the signal gets distorted.can anyone tell me the reason for that and how to avoid the distortion? thanks,

Homework Statement A string with no initial displacement is set into motion by being struck over a length 2s about its center. This center section is given an initial velocity v_0. Describe the subsequent motion. Homework Equations Coupled oscillations... The Attempt at a Solution...

Homework Statement I have three coupled pendulums: each of identical mass, and hung fromt the ceiling with identical massless rod. They are connected by identical massless springs. \phi_{1}, \phi_{2}, and \phi_{3} represent their angles from the vertical, hanging position. Find these...

Hi everyone Homework Statement Take a look at the drawing. Now I found out the differential equation for this is: \mu \vec{r}''=-k \vec{r} mu is the reduced mass Now I shall show, with using the generel solution for this differential equation (in cartesian coordinates), that the...

Homework Statement Set up the equations of motion for the system shown in Fig. 4.16. The relaxed lengths of the two springs are l1, l2 . Separate the problem into two problems, one involving the motion of the center of mass, and the other involving the "internal motion" described by the two...

Hi, I have to modelize the buckling of a column and I've come up with this system: N'(x) + N(x) \theta ' (x) \theta (x) - Q \theta ' (x) + f = 0 Q'(x) + N(x) \theta ' (x) + Q \theta ' (x) \theta (x) = 0 with f a constant The coefficients (thetas) are not constants. I've written it...

Hi all, I am currently having trouble with an exercise: writing the propagator of a particle coupled to a magnetic field. So the lagrangian is L_A (\vec{x},\dot{\vec{x}}^2) = \frac{m}{2}\dot{\vec{x}} + e\vec{A}.\dot{\vec{x}} And it says that I should solve it in two different ways: -by writing...

Hello and thank you in advance for anyone taking time to respond. I working on formulating a theory for elastodynamics, but my statistics is admittedly weak. I'm trying to find a relationship between a non random function and a random function, for example, the covariance. <A(x)B(y)>=some...

Hello, It has taken me a long time to try and figure out what a system of coupled PDEs actually IS-and I still can't get a straight answer. For example I have a system: \dot{M}=-LvM \dot{N}=-Lv+wN where here ,L, represents the lie derivative and M, N , v, w, are all elements of...

Homework Statement http://imgur.com/2KIhk Hi! If you please look at the image. I have already determined the equations of motion. They are as follows: Ma1 = 2kx1+kx2 Ma2 = -2kx2+kx1+kx3 Mx3 = -2x3 +kx2 Now... what I don't understand is how does this physically happen? If...

Homework Statement I'm trying to derive an expression for the angular frequency of a set of springs hanging vertically down with masses in between them. 3 cases: 2 equal masses and springs. 2 different masses and equal springs 3 equal masses and springs Homework Equations ω0=√(k/m)...

Homework Statement The problem statement is given in its entirety in the attachment. 2. Homework Equations / 3. The Attempt at a Solution Unfortunately, I have no clue where to start. :( I should add that due to extenuating circumstances I've missed quite a bit of physics instruction...

Homework Statement Solve the coupled mass spring problem for two different masses. Similar to the Shankar example: (d/dt)2x1=-2*w1*x1 + w1*x2 (d/dt)2x2=w2*x1 -2*w2*x2 where w1= k/m1 w2 = k/m2 Homework Equations Eigenvalue problem: UX=uX Diagonalization: A=UDUt Exponential...

I am struggling with whether or not to define the following system as coupled: Using LaTeX (reload if it doesn't display properly) \ddot{x}+A*x=0 \ddot{y}+A*y=0 \ddot{z}+A*z=0 where A is a known constant equal to A=\sqrt{x^2+y^2+z^2} So, what do you think?

Homework Statement Express y'' + 5y' - 24y = 0 as a system of couple first order DEs, find the eigenvalues of the system and the nature of the critical point at the origin. As well as find the general solution to the system of coupled equations and sketch some trajectories in the phase...

I am currently revising over some past papers and this question has come up which I am having problems with. My notes don't show how to solve this and I don't have any worked examples. So far from looking on the internet, I have seen two methods. The first is using an equation for energy and...

this is a system of three masses attached to a string, hanging on two fixed pulleys. I want to find the equation of motion of the middle mass, given the initial condition P(0)=X Assuming all friction, stretching of the strings, and momentum of the pulleys are negligible. The string has...

Homework Statement This is not so much a homework problem but a part of a project I'm working on. So in just a few words; what I have (at time t=0) is a discrete state (half simple harmonic oscillator) connected to a wire with continuous states. These states are coupled by a complex...

Homework Statement I don't know how to type math equations of I have included a image file. Take initial conditiona as [0 1] Homework Equations The Attempt at a Solution No idea

I have the following system of first order PDEs \begin{array}{rcl} \frac{\partial v}{\partial t}+v\frac{\partial v}{\partial x} & = & -\varepsilon\gamma^{-3}(v)E \\ \frac{\partial n}{\partial t}+\frac{\partial}{\partial x}(nv) & = & 0 \\ \frac{\partial E}{\partial t}+E & = & nv \end{array}...

Homework Statement given a general system, \frac{df}{dt}=k_{1}g(t) \frac{dg}{dt}=-k_{2}f(t) How could one solve for f_{analytic}. I've used wolfram, so I know what they look like. But how does one begin to solve for them? Further, how does one find the eigenvalues, eigenmodes...

For the solution to this problem, I have reduced the number of equations down from 17 to 6. Due to algebra reasons, these equations cannot really be solved symbolically (MAPLE tried, and return four full pages packed with symbols, just for one equation). These three equations need to be solved...

Homework Statement (A) [PLAIN]http://remote.physik.tu-berlin.de/farm/uploads/pics/Gekoppeltes_Pendel_01.png What happens when you swing pendulum P1? (B) How does the position of the spring affect the outcome? (C) If the length of the string of one pendulum was longer than the...

I have the equations \frac{l}{u^{2}} \frac{du}{dx}=constant and \frac{1}{u} \frac{dl}{dx}=constant. By "eyeball", I can say the solution is l \propto x^{n} \ and \ u \propto x^{n-1}. I can't see how I could arrive at these solutions 'properly', if you know what I mean

Homework Statement The problem can be found here. http://wopho.org/dl.php?id=17&dirfile=selection-problem/helical_rope.pdf" I am attempting to solve part 3. Homework Equations The Lagrangian of the system is: L= \frac{m\dot{x}^2}{2}+\frac{mr^2\dot{\theta}^2}{2}-k \left(...

Hey folks I'm looking for a way to find the characteristic equation for a second order coupled system of differential equations such as... \ddot{x} + A\dot{y} + Bx = 0 \ddot{y} + C\dot{x} + Dy = 0 Where x and y are functions of time. I know I can solve it by setting x and y to standard...

Homework Statement A 3-storey building can be modeled as a system of coupled masses and springs as showen in attached document. Where mi is the mass of each floor, ki is the spring constant, xi is the displacement of each floor, and ci is the damping coeffcient. Homework Equations I...

Can anyone please suggest whether I can use MATLAB ode45 for the numerical solution of the following equations? mx ̈+ c_x x ̇ + k_x x= F_x0+ μ(v_r ) (K 〖VB〗^2 y ̇/v) sgn(v_r ) my ̈+ c_y y ̇+ k_y y= F_y0+ (K 〖VB〗^2 (y/v) ̇ ) Where, m, c_x, k_x, c_y, k_y, F_x0, F_y0, K, v are known...

Homework Statement If we have the following partial decay chain: N1 -> N2 -> N3 where N1 is the number of nuclei of species 1, etc. and N1 -> N2, not via a decay but by the reaction such as N1 + neutron -> N2 + photon and we know this rate of formation of N2, say 'a'. I then get the...

If we have the following partial decay chain: N1 -> N2 -> N3 where N1 is the number of nuclei of species 1, etc. and N1 -> N2, not via a decay but by the reaction such as N1 + neutron -> N2 + photon and we know this rate of formation of N2, say 'a'. I then get the following rate...

Hello I have a question about coupled oscillators and what initial conditions affect what constants of integration. In the book I have, A.P. French Vibrations and Waves, the guesses at solutions are chosen at random and sometimes do include a phase shift, while sometimes they dont. For...

Homework Statement Two equal masses are held on a frictionless track by 3 equal springs, attached to two rigid posts. If either of the masses is clamped, the period (t=2pi/w) of one oscillation is three seconds. If both masses are free, what is the periods of oscillation of both normal...

I am trying to solve a problem (not homework, too old for that! lol!) which involves the time dependent schrodinger equation for magnetic moment in time-dependent magnetic fields. I end up with the following that needs to be solved: x' = -i*(b*t-a*t^2)*x - i*c*y y' = -i*c*x -...

So I am doing a FEA simulation on Joule heating of a busbar and consequently its thermal expansion. So the idea is that if I only use 1 study step, and have the temperature output from the joule heating as an input for thermal expansion, COMSOL calls this as a weakly coupled system, and they...

Hello there! Could someone please help me with setting the starting equations for coupled oscillators. I'm having serious troubles with setting the +- signes right (yes, more than with the differental equations :) ). OFF TOPIC: any reading materials about problems with signs in physics will...

greetings, At high frequency (more than 20kHz) the reactance of capacitor is very small and act as short circuit.this increase the loading of next stage.whats the meaning of increse of loading in next stage? RC coupled two stage amplifier circuit is here-...

I am trying to understand how leaky cables work, and especially those that permit higher frequencies (I think about 2.4GHz), but I am quite new to electromagnetics in general. For clarification, leaky cables are usually coaxial cables that have apertures in their outer conductor from where an...

Homework Statement Two masses attached via springs (see picture attachment). k_n represents the spring constant of the n^{th} spring, x_n represents the displacement from the natural length of the spring. There are two masses, m_1 and m_2.2. The attempt at a solution My problem is formulating...

I'm doing a research project on collisions and I've come across a part of my theory that requires solutions to coupled damped oscillators. Could anyone please refer me to some text on 2 coupled damped oscillators which isn't extremely math heavy and has conceptual explanations of the...

Homework Statement Hey there, We assume that the spring got no mass and there are no frictions. If you want to push down just as hard on m1 that if you release ... m2 will be just about to jump and leave the table? Homework Equations Newton and Hooke are our very best friends...

Hello, Are all endothermic reaction take their energy from a coupled exothermic reaction? Is it possible that an endothermic reaction would take it's energy from the physical process of cooloing the environment? If so- why are there so many coupled reactions in cell biology if it can just take...

Here is the equation I don't know how to solve: \begin{aligned} \left( {\frac{{{{\rm{d}}^2}}}{{{\rm{d}}{t^2}}} + \beta _1^2} \right){u_1} = {g_1}u_2^{}{u_3} \\ \left( {\frac{{{{\rm{d}}^2}}}{{{\rm{d}}{t^2}}} + \beta _2^2} \right){u_2} = {g_2}u_1^{}{u_3} \\ \left(...

Hi, I have a coupled system of ODE like: w1'' = A w2'' + B w1 + C w2 w2'' = D w1'' + E w1 + F w2 I need to solve it analytically but it seems it cannot be solved using eigenvalue method. My concern is first that if this system have sufficient equations and if so how it can be solved...