What is Oscillator: Definition and 1000 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. J

    Harmonic oscillator eigenvector/eigenvalue spectrum

    the problem is attached as an image. im having troubles with the question. I'm assuming this is an induction question? i can prove it for the basis step n=0. but I am having trouble as to what i have to do for n+1 (inductive step). any help or hints would be great!thanks
  2. T

    What is the difference between an excitable system and a relaxation oscillator?

    Homework Statement Consider the following set of differential equations: \begin{eqnarray*} \dot{u} & = & b(v-u)(\alpha+u^2)-u \\ \dot{v} & = & c-u \end{eqnarray*} The parameters b \gg 1 and \alpha \ll 1 are fixed, with 8\alpha b < 1. Show that the system exhibits relaxation...
  3. C

    Analogue Oscillator: 2 Applications Explained

    What are 2 applications of an oscillator circuit, I need help with this!? I can only find one... :frown: thanks for any help
  4. E

    Half-Harmonic Oscillator to Full-Harmonic Potential

    Homework Statement This problem was already answered: "I have to find the allowed energies of this potential: V(x)= (mω2^2)/2 for x>0 infinite for x<0 My suggestion is that all the odd-numbered energies (n = 1, 3, 5...) in the ordinary harmonic osc. potential are...
  5. Femme_physics

    Engineering Trying to explain how a Relaxation Oscillator UJT circuit works

    http://img689.imageshack.us/img689/7084/ujte.jpg This is a Relaxation Oscillator circuit with UJT. I need to A) Explain what is UJT, explain its relation ratio of η for the UJT, and explain what Vp is. And in B) Explain how does the circuit work, and what is the output (or turnout) of the...
  6. P

    Oscillator strength of mixed LH- and HH-excitons

    This concerns calculation of Rabi splitting of exciton polaritons when the exciton states are mixed but the mixing is known, i.e., the coefficients of the mixed states are known. I read from a thesis that the Rabi splitting is proportional to the square root of the oscillator strength. Is...
  7. T

    Harmonic oscillator analytic vs. numerical

    Homework Statement trying to write a program in C++ to calculate the solution of a damped harmonic oscillator and compare with the exact analytic solution. i am using the classic 4th order Runge-Kutta, which I'm fairly sure is programmed right. Homework Equations m\ddot{x} + c\dot{x}...
  8. R

    Build RLC Oscillator Circuit: Real-Life Examples & Falstad Simulation

    Hello I am trying to understand how exactly an oscillator circuit work and how to build one. So I was palying around in falstad and made this: the following is link. tried to get around spam filter so.. write without spaces h t t p s : / / w w w . f a l s t a d . c o m / c i r c u i t /...
  9. P

    Can anyone please tell me more about local oscillator?

    Local oscillators that is used in RF transmitters for AM modulation.Any help is appreciated. Thanks !
  10. L

    Ground state energy of particle in quantum harmonic oscillator.

    Homework Statement Consider a quantum mechanical particle moving in a potential V(x) = 1/2mω2x2. When this particle is in the state of lowest energy, A: it has zero energy B: is located at x = 0 C: has a vanishing wavefunction D: none of the above Homework Equations The...
  11. L

    Mass Spring Oscillator question

    Homework Statement A mass of 0.3kg hangs motionless from a vertical spring whose length is 0.8m and unstreteched length is 0.65m. The mass is then pulled down so the spring has the length of 0.9m and given an initial speed upwards of 1.2m/s upwards. What is the maximum length of the...
  12. S

    Coupled Quantum Harmonic Oscillator

    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...
  13. S

    Series expansion of a harmonic oscillator

    Homework Statement Use a series expansion ψ=A0x0+A1x1+A2x2+... to determine the three lowest-order wave functions for a harmonic oscillator with spring constant k and mass m, and show that the engergies are the expected values. Homework Equations Series expansion given above Time...
  14. S

    2 DOF oscillator max force reponse

    (NOTE, this is not a homework problem, but it sure seems like one) Hello, I am mounting a component onto structure and I need to determine the maximum force input into the component. My system can be represented by a base driven two degree of freedom oscillator...
  15. S

    2 DOF oscillator max force response

    Hello, I am mounting a component onto structure and I need to determine the maximum force input into the component. My system can be represented by a base driven two degree of freedom oscillator: http://www.freeimagehosting.net/newuploads/xowmr.png I need to determine the force...
  16. E

    Harmonic Oscillator in Dirac Theory

    Hello everyone, i'm looking for anypaper or such kind of thing that explain the resolution of the harmonic oscillator in the Dirac Theory. I have worked with the exact spin symmetry. I feel like a fish out the water and I'm sure that there are lot of bibliography about this area, but i...
  17. H

    Expected Value of Hamiltonian in a Forced Quantum Harmonic Oscillator.

    Homework Statement Given an initial (t=-∞) Fock state , \left|n\right\rangle, and a function f(t), where f(±∞)=0, show that for a Harmonic Oscillator perturbed by f(t)\hat{x} the difference \left\langle H(+∞) \right\rangle - \left\langle H(-∞) \right\rangle is always positive.Homework Equations...
  18. P

    Electronic Oscillator: AC or DC Output?

    i have a wien bridge oscillator by using ±15V power supply. its output is sine wave. but i have a question. is the output become ac or still dc while it is oscillate with 10kHz?
  19. W

    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...
  20. S

    Harmonic Oscillator - Modeling and Observations

    Homework Statement Consider a steel spring with the property that it extends by 10cm (0.1m) in equilibrium when you attach the upper end of the spring to a fixed support and hang a weight of 100g (0.1kg) at the springs lower end. 1) Use the equation for the harmonic oscillator to determine...
  21. P

    Motion equation for harmonic oscillator

    Homework Statement A mass m is attached to a spring of stiffness k. The spring is attached to the ceiling and the mass hangs freely from the spring under the force of gravity. (a) Derive the equation of motion for this system. (b) Find an expression for the equilibrium position of the...
  22. E

    Clasical and quantum harmonic oscillator - correspondence principle

    At classical harmonic oscillator, total energy is proportional to square of frequency, but at quantum harmonic oscillator, total energy is proportional to frequency. Are those two frequencies the same? How it is with transition from quantum harmonic oscillator to classical harmonic oscillator...
  23. G

    Need help understanding how an R-C oscillator works

    Hoping someone can help me with some basic questions about resistor-capacitor oscillator (timer) circuits. I can put them together, I see them working, but I don't understand why! In the circuit in the attached drawing, if one installs the correct values of resistor and capacitor, I know...
  24. H

    Potential energy harmonic oscillator

    Hello, I have this problem with deriving the formule from de definition of potential energy Picture show a mass-spring system in rest position: In general potential energy can be written as dot product: \frac{dE_{P}}{d\overrightarrow{y}}=-\overrightarrow{F}. Potential energy wil...
  25. C

    The rate at which a damped, driven oscillator does work

    Homework Statement Consider a damped oscillator, with natural frequency ω_naut and damping constant both fixed, that is driven by a force F(t)=F_naut*cos(ωt). a) Find the rate P(t) at which F(t) does work and show that the average (P)avg over any number of complete cycles is mβω2A2. b)...
  26. F

    Voltage controlled oscillator

    Hi,I am currently doing my project of designing a 100Mhz Voltage controlled oscillator,but i am stucked in the oscillator part,can anyone tell me about the oscillator between the feedback model method and negative resistance method?how to identify the result of my oscillator is work by using ADS?
  27. D

    Harmonic Oscillator Design - controls approach

    I have a question regarding an oscillator design from a controls perspective. An ideal harmonic oscillator has just 2 poles, both on the imaginary axis, and their location along the axis determines the frequency of oscillation as well as the amplitude. Now, please correct me if this is...
  28. V

    Time dependent perturbation for harmonic oscillator

    Homework Statement I'm looking at the 1d harmonic oscillator \begin{equation} V(x)=\frac{1}{2}kx^2 \end{equation} with eigenstates n and the time dependent perturbation \begin{equation} H'(t)=qx^3\frac{(\tau^2}{t^2+\tau^2} \end{equation} For t=-∞ the oscillator is in the groundstate...
  29. teroenza

    Damped oscillator energy dissipated per cycle.

    Homework Statement Sinusoidal driving force driving a damped oscillator (mass = m). Natural frequency is assumed to equal the drive frequency = w Time has elapsed to the point any transients have dissipated. Show that the energy dissipated by the damping force [F=-bv] during one cycle is...
  30. Hepth

    Thought Prob : Regenerative Damping of a Simple Harmonic Oscillator

    So I was just thinking about regenerative braking, piezoelectric sensors/strain gauges, magnetic-induced currents etc. and I thought of a question that would make a simple/decent discussion/practice in general engineer/physics (lots of /'s) Suppose you have a simple harmonic oscillator :: WALL...
  31. J

    Two dimensional asymmetric harmonic oscillator

    Let's say I have a 2D harmonic oscillator: Homework Statement The potential is of course defined by: V = 1/2m(Omegax)x^2 + 1/2m(Omegay)y^2 Homework Equations Generally when doing a harmonic oscillator we find that in two dimensions the energy is just: (Nx+Ny+1)hbarOmega is the energy. How...
  32. A

    Harmonic Oscillator with random number-mathlab

    Hello there, lets say i have a harmonic oscillator equation d^2x/dt^2 = -w^2 x = -Asin(wt) w=frequency, A=amplitude..how can i plot this equation for w^2=1, x(0)=1? and what if the equation contains random number d^2x/dt^2 = -w^2x+Bn, n=gaussian random number with mean value equal to zero...
  33. Demon117

    Perturbed harmonic oscillator

    Homework Statement I showed earlier this semester that in the presence of a "constant force", F_{o}, i.e. V=-Fx, that the eigenvalues for the Harmonic oscillator are shifted by \frac{F^{2}}{2m\omega^{2}} from the "unperturbed" case. It was also discussed that x\rightarrow...
  34. G

    Harmonic Oscillator: Evaluating Ground State Probability

    Homework Statement Using the normalization constant A and the value of a, evaluate the probability to find an oscillator in the ground state beyond the classical turning points ±x0. Assume an electron bound to an atomic-sized region (x0 = 0.1 nm) with an effective force constant of 1.0...
  35. L

    Harmonic Oscillator (not sure where to post)

    I'm not understanding the following formula. I'm a computer programmer and was given a set of formulas to have an application to solve; however I'm not completely understanding how this works. I'm just looking for a step by step way to solve this and an explanation on why there are 3 assignment...
  36. A

    1D oscillator solving for Amplitude

    Homework Statement You are told that, at the known positions x_{1} and x_{2}, an oscillating mass m has speed v_{1} and v_{2}. What are the amplitude and angular frequency of the oscillations? Homework Equations x(t) = Acos(wt - \delta) v(t) = -Awsin(wt -\delta) w =...
  37. J

    Transposing Terms for an Isotropic Oscillator

    Homework Statement The problem asks us to find the equation for an isotropic oscillator in the form of an equation for an ellipse. I'm in PHYS 212, Analytic Mechanics. Homework Equations x=Acost(ωt) y=5Acos(ωt-.6435) The equations I found for x and y. The Attempt at a...
  38. H

    Perturbation of 2D Oscillator along one axis

    The problem given is a perturbation on the two dimensional harmonic oscillator where the perturbation is simply: H'=-qfy. It seems that all of the elements of the matrix H' are zero and so constructing a diagonal matrix in the subspace is eluding me. Any ideas?
  39. L

    Work done by damping, harmonic oscillator, help?

    Ok here's the question: A body m is attached to a spring with spring constant k. While the body executes oscillations it also experiences a damping force F = -βv where 'v' is time derivative of displacement of the body from its equilibrium position. I believe equation of motion is F =...
  40. S

    Finding degeneracy of N Quantum Harmonic Oscillator

    Hey guys, For a particular problem I have to determine the total degeneracy across N 3-D Quantum Harmonic oscillators. Given that the degree of degeneracy for a 3-D harmonic oscillator is given by: (n+1)(n+2)/2 and the Total energy of N 3d quantum harmonic oscillators is given by...
  41. F

    What is the optimal biasing network and transistor for a Clapp oscillator?

    My last attempt at building a simple oscillator did not go so well. After doing research on harmonic electronic oscillators, I finally came across one that seemed relatively simple (not a whole lot of parts) and that had an easily computed resonance frequency, the Clapp oscillator. I have...
  42. E

    Harmonic Oscillator - Mass With Initial Velocity

    For a harmonic oscillator with mass M, spring of stiffness k and displacement the force equation is: -kx = Md2x/dt2 How do you handle the situation and work out a solution for x(t) when the mass has an initial velocity. E.g. a mass dropped onto the spring?
  43. S

    Relationship betwen SHM frequency and harmonic oscillator freq.

    Homework Statement Relate the frequency of a harmonic oscillator (spring) to that of a simple harmonic oscillator (pendulum) Show all derivations. Homework Equations pendulum: f=(1/(2∏))√(g/L) The Attempt at a Solution Not exactly sure how to go about this...is it saying...
  44. S

    Driven Damped Oscillator problem

    Homework Statement Given damping constant b, mass m spring constant k, in a damped driven oscillation system the average power introduced into the system equals the average power drained out of the system by the damping force, for what values of ω does the instantanious damping power =...
  45. M

    Harmonic Oscillator Problem: Energy Levels & Ground State

    Problem: Consider a harmonic oscillator of mass m undergoing harmonic motion in two dimensions x and y. The potential energy is given by V(x,y) = (1/2)kxx2 + (1/2)kyy2. (a) Write down the expression for the Hamiltonian operator for such a system. (b) What is the general expression for...
  46. B

    I have a question if i have a oscillator pushing 7.8 Hz 144 Hz cycle

    I have a question if i have a oscillator pushing 7.8 Hz 144 Hz cycle top (polarity 288 Hz) 432 Hz bottom cycle ... What kind oscillator is this?
  47. A

    Quantum Harmonic Oscillator Question

    Hello everybody, recently in my quantum mechanical course we were introduced to the concept of the quantum harmonic oscillator. My question is: is there a physical significance attached to the fact that the classical turning points overlap with the sign change of the second derivative of the...
  48. B

    Creating a Colpitts Oscillator

    I am creating an experiment to show how wireless energy can be transferred through resonantly tuned lc circuits. In order for this to work i need an oscillator. I have been told to try a colpitts oscillator. I have looked online and found a few sites showing calculators and schematics for these...
  49. A

    Overshooting in a critically damped oscillator

    How can we tell whether a given v0 will cause an oscillator to overshoot the equilibrium? If the velocity high enough, we know the oscillator will overshoot and return to equilibrium. But if v0 is low, the system would act like it came from a point a bit farther out and not overshoot (right?)...
  50. maverick280857

    Is the ground state of a harmonic oscillator unique?

    Hi, In one of my advanced quantum mechanics classes, the instructor posed a problem, namely to show that the ground state of a one dimensional quantum harmonic oscillator is unique, without getting into differential equations. I know that the equation a\left|0\right\rangle = 0 when...
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