Coupled oscillator Definition and 32 Threads

For the record, here is the lecture I am speaking of. Consider a double pendulum. I'm going to skip the setup of the problem and jump to the system of differential equations $$m\ddot{x}_1=-\frac{3g}{l}x_1+\frac{g}{l}x_2\tag{1}$$ $$m\ddot{x}_2=\frac{g}{l}x_1-\frac{g}{l}x_2\tag{2}$$ where...

Here is the actual lecture. The equations of motion for ##m_1## are $$m_1\ddot{x}_1=-T_1\sin{\theta_1}+k(x_2-x_1)\tag{1}$$ $$m_1\ddot{y}_1=T_1\cos{\theta_1}-m_1g\tag{2}$$ The lecture says that we are using small angle approximations $$\sin{\theta_1}\approx\theta_1\tag{3}$$...

The masses are ##m_1## and ##m_2##. We measure the displacements of each mass as follows When the blocks move horizontally, they will move vertically as well, because the length of the pendulums remains fixed. Because vertical displacement is second order in the ##x_j##'s, $$y_j\approx...

Idea: Given a system of two coupled oscillators in which 2 masses are connected to a spring in the middle. Each of the two masses is coupled to another spring on the left and right, which have fixed ends but are not connected to each other. So we have 3 springs, two masses and the springs also...

If a Hookean spring-mass system is made from one mass and a spring, to produce a system with a particular oscillation frequency, it's not a problem to use the propagation of errors concept to find how this frequency responds to small errors in the mass and spring constant. If a chain of...

Hi, First of all, I'm not sure at all how to start this question. I found the eigenvectors in a previous question, but I'm not sure if I need it to solve this one. I think I need to use the expression for the position and velocity. ##a_n = C_n cos (\omega_n t + \alpha_n)## ##v_n = -\omega_n...

Hi, I have to find the eigenvalues and eigenvectors for a system of 3 masses and 4 springs. At the end I don't get the right eigenvalues, but honestly I don't know why. Everything seems fine for me. I spent the day to look where is my error, but I really don't know. ##m_a = m_b = m_c## I got...

Hi, I know there's are 2 normal modes because the system has 2 mass. I did the Newton's law for both mass. ##m\ddot x_1 = -\frac{mgx_1}{l} -k(x_1 - x_2)## (1) ##m\ddot x_2 = -\frac{mgx_2}{l} +k(x_1 - x_2)## (2) In the pendulum mode ##x_1 = x_2## and in the breathing mode ##x_1 = -x_2## I get...

This is a question from an exercise I don't have the answers to. I have been trying to figure this out for a long time and don't know what to do after writing mx''¨(t)=−kx(t)+mg I figure that the frequency ω=√(k/m) since the mg term is constant and the kx term is the only term that changes. I...

1. Derive the wave equation for longitudinal vibrations in an extended 1-D system of masses and springs. The average distance between masses is D [m], the spring constants are K [kg/s2 ], and the masses are M [kg]. b) Determine the wave speed c as a function of D, K, and M. Verify that it has...

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 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: $$...

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...

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...

Homework Statement Two identical undamped oscillators, A and B, each of mass m and natural (angular) frequency $\omega_0$, are coupled in such a way that the coupling force exerted on A is \alpha m (\frac{d^2 x_A}{dt^2}), and the coupling force exerted on B is \alpha m (\frac{d^2...

How does one go about plotting the effects of the frequency of the driving force vs the amplitude of the masses in a system such as the one pictured below? Assume that I have already figured out what my two angular frequencies are, and the amplitues under driven force (the actually equations...

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...

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...

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 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 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(...

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...

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...

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 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...

Homework Statement WIthin the framework of an idealised model, let a square plate be a rigid object with side "w" and mass "M", whose corners are supported by massless springs, all with a spring constant "k". The string are confined so they stretch and compress vertically with upperturbed...

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

Homework Statement A thin hoop of radius R and mass M oscillates in its own plane with one point of the hoop fixed. Attached to the hoop is a small mass M constrained to move (in a frictionless manner) along the hoop. Consider only small oscillations, and show that the eigenfrequencies are blah...

Homework Statement An object of mass m and another of mass M = 2m are connected to 3 springs of spring constant horixontally. The displacement of the two masses are defined as x and y. When x = y = 0, the springs are unextended. a) Write down the two coupled equations of motion...

Hello I'm having a bit of trouble with analysing some of the coupled oscillator questions in terms of the energy functions. Here is a coupled oscillator diagram: http://img356.imageshack.us/img356/28/coupledlagr4fx.png Now for this one my main problem is that I don't know how to come up...

I am given a set up with two pendulums of unknown mass m, of length =.4 meters. They are connected together with a spring of unknown spring constant k. It says when one of the bobs if fixed in place the other has a period of 1.25 seconds. I am then asked to find the period of each normal mode...

Could some one please help me understand the current flow in this circuit (electron flow theory)... specifically, how does the capacitor charge, and how do the two transistors open/close? So far this is what I think... The current leaves the negative terminal, splits up into both branches...