Coupled Definition and 414 Threads

I am tasked to answer the following question on the subject of coupled pendulums: QUESTION: The Antisymmetric and symmetric normal modes can be superposed to obtain new solutions. Can ANY solutions be written as a superposition of these two modes? Justify your answer. Hint: Is a solution...

Homework Statement http://img849.imageshack.us/img849/6315/63685525.jpg The Attempt at a Solution (a) I think since i=dq/dt we will have: L_1 \frac{d^2q_1}{dt^2} + R_1 \frac{dq_1}{dt}+ \frac{q_1}{c_1}+ \left( \frac{q_1-q_2}{C} \right) = 0 L_2 \frac{d^2q_2}{dt^2}+ R_2 \frac{dq_2}{dt} +...

Hey, I need your help to solve the following set of coupled differential equations numerically. dn(t,z)/dt=I^5(t,z)+I(t,z)*n(t,z) dI(t,z)/dz=I^5(t,z)-α(n(t,z))*I(t,z) where I(t,0)=I0*exp(-4ln2(t/Δt)^2) and n(t,0)=0 and n(-certrain time,z)=0. Some constant parameters I did not show...

Problem: Model the coupled ode system for a motor: Equations: dVc/dt=(-1/C)*Il+(1/C)Is dIl/dt=(1/L)*Vc-(R/L)*Il I have been given the values of L=1e-3, R=50, Is=10.0A and C is to be designed by trial and error. I have been able to write out the function, by assigning Vc=x(1) and Il=x(2)...

Homework Statement I need to transform the Hamiltonian of a coupled Harmonic Oscillator into the sum of two decoupled Hamiltonians (non-interacting oscillators). Homework Equations H = H1 + H2 + qxy, where H1=0.5*m*omega^2*x^2+0.5m^-1P_x^2 and H2=0.5*m*omega^2*y^2+0.5m^-1P_y^2, and q is...

1. Just going through some material about parametric amplifiers but I have difficulties to see where the solution comes in given text. In equations it is assumed undepleted pump wave and in equations there is loss caused by linear absorption for signal and idler. 2. p.s. There is a...

3. Two train cars are to be coupled on the tracks. One of the cars, say A is initially at rest. The other car, say B is traveling at a speed v toward A: Car B is empty, whilst car A is full of pig iron and has a mass of 102mB: After coupling, the two cars travel a distance of 20 meters before...

Homework Statement \frac{dx}{dt}=\gamma y \frac{dy}{dt}=-\gamma x solve for x and y Homework Equations The Attempt at a Solution I know how to solve it by substitution(without using matrix) I know how to solve a coupled second order differential equations in matrix form, but not...

Homework Statement Just click the link, The image is huge, so I did not use IMG tags. http://i.imgur.com/zWNRf.jpg Homework Equations Let's see, The rotational kinetic energy of a body is given as K = \frac{1}{2}Iω^{2} for a point mass, I = mr^{2} for a rigid rod rotating at it's end...

I have been going through the ac signals coupled by a capacitor to a dc network.. Using superposition principle.. for solution it was shown that both bulk resistance and dynamic resistances for the diodes used are required... Why is this happening.. Since to what i know bulk resistance is...

Homework Statement Equations: \frac{dv_{1}}{dt} = -v_{1} - \frac{2v_{2}}{3} + 1 + \frac{t}{3} \frac{dv_{2}}{dt} = -2v_{2} - 1 - 2t Initial Conditions: v_{1}(0) = 6 v_{2}(0) = -6 2. The attempt at a solution Defined the following: v(t) = [ v_{1}(t) v_{2}(t) ] \frac{dv(t)}{dt} = [...

Hi eveyone. I really need your help for this project that I will be undertaking soon. But there is much I still don't understand and my lecturers aren't around to help. The setup that I'm envisioning is like this-- Source(230V 50hz) connects to signal generator, signal generator to 1st RLC...

Coordinate System of Coupled Oscillators and "4D" Phase Space representation So, I've modeled the interaction between two cantilever beams with the kinetic and potential energies shown in the above figure. The cantilevers are very stiff and have a small oscillation amplitude, so they can be...

We've been asked to solve this system of equations dW/dt = = αW−βV dV dt = −γV+δW by proposing that W (t) = A sin(ωt) + B cos(ωt) V (t) = C sin(ωt) + D cos(ωt). so I've differentiated both W(t) and V(t) to give W'(t) = ωA cos(ωt) - ωB sin(wt) and V'(t) = ωC cos(ωt) - ωD sin(wt) and replaced...

Hi Consider a small system A which is described by quantum mechanics. A large system B is surrounding A and this large system is described by classical physics. What kind of interactions has the system B to the small qm system? Compared to B is A very small so I guess one can neglect...

Hi, I am trying to simplify the following equations to get a relationship involving just \eta : 1) \nabla^2 \phi(x,z,t) = 0 for x\in [-\infty,\infty] and z\in [-\infty,0] , t \in [0,\infty] subject to the boundary conditions 2) \phi_t+g \eta(x,t) = f(x,z,t) at z=0 3)...

Consider a system of coupled differential equations x'=5x-y where x(0) = 6 y'=-x+5y where y(0)=-4 a) Show that the parametrised curve (x,y)= r(t)=(exp(4t) + 5exp(6t), exp(4t) - 5exp(6t)) How would you go about showing this?

What is the difference between Multi-Core Processors and Coupled Single-Core Processors? Are they the same thing?

Homework Statement A system is connected as follows, going vertically downwards: (ceiling)-(spring with constant k)-(mass 1)- spring with constant k)-(mass 2) Let x be the displacement from the equilibrium position of mass 1, and let y be the displacement from the equilibrium position of...

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...

Hi Homework Statement Given is a system containing to masses m1 and m2 which are connected by a spring with spring constant k.Oscillation and translation is restricted to one dimension only. Homework Equations euqation of motion The Attempt at a Solution So, I can find...

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...

I'm a bit unclear on exactly what a coupled state really means and how to represent it, so here's what I have: Homework Statement Consider the coupling of two spinless l=1 particles, What possible product states |1\, m_1 \rangle \otimes |1\, m_2 \rangle are there and what possible coupled...

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...

Homework Statement A string of length 3L and negligible mass is attached to two fixed supports at its ends. The tension in the string is T. (a) A particle of mass m is attached at a distance L from the left end of the string. What is the period for small transverse oscillations of m...

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)...

while solving Lagrangian of a system to derive equations of motion in presence of a constraint, I have finally landed down to a system of 3 coupled ODEs , where i have two variables(x and y) and 1 Lagrange multiplier. ODEs are of order 4,3 and 1 respectively. L1(x,y)=lambda L2(x,y)=0...

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...

My quantum mechanics teacher give me the following problem: "Find eigenvalues of the following system: two different particles of mass m in a harmonic oscillator coupled by attractive potential V(x1,x2)=beta*abs(x1-x2)." Now, I know that standard solving method for this kind of problem is...

Homework Statement The pulley is essentially weightless and frictionless. If M1= 10.0 kg and the second mass M2 weighs 98.1 Newtons, what is the tension in the rope and the acceleration of M1 ? Homework Equations FT=mg F=ma FT = tension m=mass g=gravity (9.81) a=acceleration The Attempt at a...

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...