What is Oscillators: Definition and 158 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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  1. shanepitts

    Inquiry about Damped Oscillators

    Hello, I have two quick inquiries related to my studies on analytical mechanics. The first is I don't quite fathom how a full-width-half-maximum of the resonance of a forced and damped oscillator behaves in relation to the Q-factor?? And the second is does the amplitude of a forced and...
  2. PsychonautQQ

    Understanding Angular Displacement in Weakly Damped Harmonic Oscillators

    Hey PF. This isn't a homework question and I'm hoping this is the right place to ask it, sorry if it isn't! In the case of a weakly damped harmonic oscillator driven by a sinusoidal force of the form Fe^(iwt). The form of the differential force equation of motion is then given by ma + cv +kx =...
  3. EinsteinKreuz

    Barkhausen tubes and other unicomponent oscillators

    So in my insatiable curiosity about electron tubes(I've been struggling to find a comprehensive textbook that discusses them-any title suggestions?)I came across the Barkhausen-Kurz Oscillator. So my questions is as follows: 1. What is the equation(based on applied voltage and current) for...
  4. Z

    Physics HW Problems HELP (Mass-Spring Oscillators)

    I am really stressed because I missed a week of school and have this online assignment due tomorrow with a ton of problems, and my biggest problem is I am not even sure if I know the equations needed to solve this stuff, if I do I just can't piece it together. 1. An elastic cord oscillates up...
  5. Runei

    Coupled driven and damped oscillators

    Hello, I'm trying to analyze a system of elastically coupled oscillators, whose masses are all the same, using Fourier expansion. So the differential equation I am looking at right now is of the form m\frac{d^2\hat{y}_k}{dt^2} + \gamma\frac{d\hat{y}_k}{dt} - \kappa\Delta^2\hat{y}_k =...
  6. F

    Harmonic Oscillators: Resonance Bandwidth & Frequency Range

    Show that the resonance bandwidth corresponds to the frequency range for which –1 < tan χ < +1. (The resonance bandwidth is the range for which the average power is greater than 0.5 times the peak power.) I'm pretty damn stumped with this.
  7. E

    FPGA-Based System Design with Multiplexed Ring Oscillators

    Hello Sir, I am PG scholar in VLSI design.I am doing my project on FPGA based system in that i have to used ring oscillator.From number oscillator i need to choose two oscillator based on multiplexer.Can anyone tell me how it is?
  8. M

    Kinetic Energy in terms of Conjugate Momenta

    Thanks if you take the time to read this. Homework Statement Homework Equations The Attempt at a Solution The problem I'm getting is that I'm not getting the kinetic energy diagonal when I convert to the coordinates that diagonalize the potential energy. If you scroll all the way down you...
  9. D

    Lattice of 1D anharmonic oscillators (Cannonical Ensemble)

    Homework Statement I have a system of N non-interacting anharmonic oscillators whose potential energy is given by, V(q) = cq^2 -gq^3 -fq^4 where c,f,g > 0 and f,g are small. Homework Equations The Hamiltonian is given by, H = \sum_{i=1}^N \big ( \frac{p^2_i}{2m} + V(q_i) \big )...
  10. F

    Two-dimensional oscillators

    Homework Statement A puck with mass m sits on a horizontal, frictionless table attached to four identical springs (constant k and unstreched length l_0). The initial lengths of the spring a are not equal to the unstretched lengths. Find the potential for small displacements x,y and show that...
  11. F

    Question Regarding Armstrong-type Oscillators

    So a little background: I am trying to construct a superhet radio with an oscillator producing a harmonic-rich output that can be electrically coupled to a mixer, the idea being one of the harmonics can heterodyne with the RF signal. After doing research regarding the construction of...
  12. V

    Quantum Mechanics: Coupled Electric Harmonic Oscillators

    Hi I am doing this completely out of self interest and it is not my homework to do this. I hope somebody can help me. Homework Statement In the book Biological Coherence and Response to External Stimuli Herbert Fröhlich wrote a chapter on Resonance Interaction. Where he considers the...
  13. N

    Coupled oscillators analog to EIT - do I miss something?

    Hi, I have posted this question to "classical physics" forum, but now I think this forum might be more appropriate. I have no idea how to move the thread here, so here is a copy.. The question seems trivial, but I want to check if I miss something. Homework Statement I'm trying to...
  14. I

    System of N classical anharmonic 3d oscillators

    1. Calculate the internal energy of a system of N classical anharmonic tridimensional oscillators of potential energy V(r) = k*(r^a) with k>0 a>0 and r = abs(r). Verify the result with a = 2 .
  15. S

    Dual harmonic oscillators connected by shear spring

    Hello everyone, looking around I have faith that the members of this forum will be able to point me in the right direction, and I apologize if it's more basic than I'm giving it credit for. I'm an experimental researcher in rock mechanics, but I've always been fascinated by elasto-dymamic...
  16. G

    Harmonic solutions as Riemannian oscillators ?

    Harmonic solutions as "Riemannian oscillators"? Has anyone heard of this idea before? Basically, you just solve the Schrodinger equation using n-dimensional spherical boundary conditions. Given n=2, you get what look like atomic orbitals. But rather than going the Born probalisitic route by...
  17. F

    How to tell if two oscillators are different

    Hi all, this is my first time on PF. As one of my projects, I had to create a program to analyze a bunch of data involving oscillators. I'm supposed to find out how many different oscillators there are within all the data. I have it pretty much done, except one part. I don't actually know how to...
  18. U

    Solving Coupled Oscillators: Find Spring Constants

    Hi, I didn't understand the exercise so I didn't do it and my teacher doesn't give the details of the solutions. If somewone can help me and explain me the steps.. it'd be great ! Three block of mass m=0.13kg are connected with three springs of constant k1 k2 k3 and Two of the normal...
  19. D

    Finding the Density of States of Radiation Oscillators

    Homework Statement Calculate the density of states if the radiation oscillators are confined to a square (i.e. in two dimensions).Homework Equations The Attempt at a Solution This was one of the questions for my Modern Physics class, (we recently covered blackbody radiation), although based on...
  20. O

    Calculate number of microstates of n harmonic oscillators

    Homework Statement Consider a system of N localized particles moving under the influence of a quantum, 1D, harmonic oscillator potential of frequency ω. The energy of the system is given by E=(1/2)N\hbarω + M\hbarω where M is the total number of quanta in the system. compute the total...
  21. K

    Lissajous figures and anisotropic oscillators

    I working on a problem involving periodic vs. non-periodic 2-d anisotropic linear oscillators. I am trying to understand why it is that for a ratio of angular velocities that is rational, the motion of the oscillator is periodic. Versus the case where the ratio of angular velocities in...
  22. E

    Exploring Oscillators: A Guide to Designing RC and LC Oscillators with Op-Amps

    i want some books about oscillators RC oscillator by op-amp LC oscillator by op-amp design it this kind of OC and thank you
  23. F

    How do I find the phase difference between two oscillators

    Homework Statement Find the phase difference between two harmonic oscillators at time t=1 Homework Equations I've already found x(t)= .4 cos(2.1t) and x(t)= .4cos((pi/2)t + pi) The Attempt at a Solution I don't really know where to begin
  24. A

    Crystal Oscillators - accuracy versus temperature

    Crystal Oscillators -- accuracy versus temperature I have done quite a lot of desk research and spoken to a few manufacturers, but I am still not clear about the specifications for crystal oscillators and I hope someone can help me out. It is a multi-part question. 1) The accuracy of an XO...
  25. R

    [coupled harmonic oscillators] old thread- need elaboration

    Hi Can someone please explain the answer to the following thread? I tried uncoupling the Hamiltonian but to no avail. https://www.physicsforums.com/showthread.php?t=602106 Thank you.
  26. U

    Generalization of the bohr rule for harmonic oscillators

    Homework Statement The generalization of the bohr rule to periodic motion more general than circular orbit states that: ∫p.dr = nh = 2∏nh(bar). the integral is a closed line integral and the bolded letters represent vectors. Using the generalized, show that the spectrum for the...
  27. O

    Determening the Period of Coupled Oscillators

    Hello everyone, I was wondering how could you determine the period of the motion of two or more coupled oscillators. For example, two oscillators have the state variable equations: x_1=A_1\cos{(\omega_1t+\phi_1)}+A_2\cos{(\omega_2t+\phi_2)}...
  28. C

    Out of 2 oscillators, which one decays to .1A first?

    Homework Statement Consider 2 oscillators (mass attached to spring on surface). For one oscillator, the surface is frictionless, but there is viscous damping (f=-bv). For the other, the surface has coefficient of kinetic friction uk, but there is no viscous damping. The masses are both pulled...
  29. S

    Output voltage of Crystal Oscillators

    I am currently building a circuit that produces a 200khz signal with a potential difference of 3 - 12 volts, depending on the force applied to a strain gauge. The input voltage is a 12V, 50hz source. With no force applied to the strain gauge, the output is to be 3V and 12V at breaking force...
  30. C

    Markov property and chemical oscillators

    Hi everybody... I've been working a bit with models of chemical oscillators and I've run into something that isn't quite clear to me. Chemical reaction systems are typically regarded as having the Markov property -- they lack memory and their evolution depends only on their current state...
  31. S

    Equation of motion for coupled oscillators

    Attached is the formula for the equation of motion for a system of coupled oscillators. Could someone please tell me what the variables and indices refer to here? Thanks! :)
  32. M

    Position operator for a system of coupled harmonic oscillators

    Hi I would like to know if I have a system of coupled harmonic oscillators whether the standard position operator for an uncoupled oscillator is valid, i.e. x_i = \frac{1}{\sqrt{2}} (a_i+a_i^\dagger)? where i labels the ions. To give some context I am looking at a problem involving a...
  33. R

    Coupled Oscillators (Electrical Circuit)

    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} +...
  34. S

    How sinusoidal oscillators produce sinusoids?

    Why/How does a linear oscillator give >>>sinusoidal<<< output? I am basically confused how the sinusoidal signal output generates from a random noise? Why sinusoidal and not something else? Can this be explained from the characteristic equation/circuit poles?
  35. T

    10 Oscillators & 8 Quanta of Energy, Dominant Configuration?

    Hello, This is my first time using this forum, I just have a quick question that I'm trying not to get too held up on by re-reading (skimming) the chapter several times. Anyways: Homework Statement "Consider the case of 10 oscillators and eight quanta of energy. Determine the dominant...
  36. H

    Coordinate System of Coupled Oscillators and 4D Phase Space representation

    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...
  37. S

    Weight of N 3-Dimensional Quantum Harmonic Oscillators

    Hey guys, The question gives us N 3-Dimensional Quantum Harmonic Oscillators with : E=ƩE(i)=Ʃ(n(i)+0.5)(h-bar)w Where h-bar is the reduced Plancks constant, w is the angular frequency, and the sum takes place over i=1 to i=3N, and (i) is subscript! Now I believe the microstates of this...
  38. T

    Difference between the Rayleigh and Van Der Pol Oscillators?

    Homework Statement I have two separate problems, but I get the same answer for each. I feel like this must be wrong. Question 1: Find the leading term of a uniformly valid (for t > 0) asymptotic expansion of the solution of the IVP \ddot{x} + \epsilon\dot{x}(x^2-1)+x = 0 \mbox{ } x(0) =...
  39. E

    Coupled Oscillators in a String

    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...
  40. B

    Harmonic oscillators and commutators.

    Homework Statement If we have a harmonic oscillator with creation and annhilation operators a_{-} a_{+} , respectively. The commutation relation is well known: [a_{+},a_{-}] = I However, if we have two independent oscillators with operators a'_{-} a'_{+} As the operators are the...
  41. C

    Simple harmonic oscillators and a pendulum clock.

    Hey physics forums, this is my first post and frankly I'm having trouble conceptualizing this problem. I know harmonic oscillation is involved, as it is a pendulum. However, I know I have to incorporate g into the s.h.o. equation and I'm not quite sure how to do that. Any help would be...
  42. F

    Coupled Q. Harmonic Oscillators

    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...
  43. E

    Quantum harmonic oscillators

    None of my textbooks seem to “close the loop” with the quantum treatment of harmonic oscillators. They all start with Plank’s assumption of quantum oscillators to explain his excellent curve fit for the black-body radiation spectrum. Then they move on to Einstein’s explanation of the...
  44. J

    Harmonic Oscillators, a general conceptual question, help please understanding?

    1)So I will describe my lab situation first, then ask my main questions. In my physics class we had an inclined air track, with 5 masses (carts) and 5 springs connected in between them. We turn on the air track to replicate a mostly 'frictionless' surface. Now we did several trials writing...
  45. B

    Exploring Bohr's Hypothesis on Harmonic Oscillators

    Homework Statement Show that bohr's hypothesis (that a particle's angular momentum must be an integer multiple of h/2pi) when applied to the three dimensional harmonic oscillator, predicts energy levels E=lh/pi w with l = 1,2,3. Is there an experiment that would falsify this prediction...
  46. Y

    Coupled Oscillators Initial Conditions and Phase

    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...
  47. W

    Coupled oscillators and normal modes question

    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...
  48. B

    MATLAB Lattice of harmonic oscillators - Matlab

    Can someone help me with my code? I am trying to generate a lattice of harmonic oscillators, and I have written the following algorithm: for n = 2:((N-1)/h) a(1,n) = -(x0-(x(2,n)-x(1,n))); x(1,n+1) = 2*x(1,n) -x(1,n-1) + (h^2)*a(1,n); t(1,n+1) = t(1,n) + (h); for i =...
  49. H

    Statistical thermodynamics - system of oscillators

    Homework Statement A system of 10 oscillators, characterised by a \beta^ parameter of ln(3/2) is in equilibrium with a heat bath. Determine the probability that the system should possesses Q quanta.Homework Equations p(Q) proportional to e^(-Beta*Q)The Attempt at a Solution I have seen a...
  50. M

    Thermodynamics: system of localized harmonic oscillators

    Homework Statement We consider a system of localized(in a lattice) weakly interacting harmonic oscillators having the non-degenerate energy levels: \epsilonv=(v+1/2)\hbar\omega v=0,1,2,... where the angular frequency is a function of the volume, \omega(V)=aN/V, where a is a constant...
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