# What is Coupled oscillator: Definition and 30 Discussions

Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. The term vibration is precisely used to describe mechanical oscillation. Familiar examples of oscillation include a swinging pendulum and alternating current.
Oscillations occur not only in mechanical systems but also in dynamic systems in virtually every area of science: for example the beating of the human heart (for circulation), business cycles in economics, predator–prey population cycles in ecology, geothermal geysers in geology, vibration of strings in guitar and other string instruments, periodic firing of nerve cells in the brain, and the periodic swelling of Cepheid variable stars in astronomy.

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11. ### Coupled oscillator: 2 masses and 3 different springs

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...
12. ### How does the electric field get removed in crystal oscillator circuits?

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...
13. ### Coupled Oscillator Homework: Normal Modes & Frequencies

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...
14. ### Question about driven coupled oscillator.

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...
15. ### Solving a Coupled Oscillator Problem: A Puzzling Exercise

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...
16. ### Solve Coupled Oscillator Problem from Goldstein's Classical Mechanics

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...
17. ### Differential equation, coupled oscillator, relative movement

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...
18. ### How Do You Solve a Coupled Oscillator Problem with Limited Physics Background?

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...
19. ### A rather interesting type of coupled oscillator.

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(...
20. ### Coupled Oscillator: Solving Initial Forces & Finding Eigenvalues

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...
21. ### Understanding Coupled Oscillator Equations of Motion

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...
22. ### Normal Modes and Frequencies of Coupled Oscillators?

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...
23. ### Coupled Oscillator Homework: Find Normal Mode Freqs

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...
24. ### Lagranguan / Coupled Oscillator

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...
25. ### Lagranguan / Coupled Oscillator

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
26. ### Solve Coupled Oscillator Homework: Find 2 Eigenfrequencies

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...
27. ### Coupled oscillator mass on spring question?

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...
28. ### Lagrangian Mechanics - coupled oscillator?

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...
29. ### How Do You Calculate the Spring Constant in a Coupled Pendulum System?

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...
30. ### How Does Current Flow in a Direct Coupled Oscillator Circuit?

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...