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. pellman

    Fermionic oscillator contradiction

    This is a question with regard to a specific step in a problem. I don't think it is necessary to elaborate the whole problem. Homework Statement Resolve this apparent contradiction. I get two different answers for Na|n\rangle Homework Equations For a fermionic oscillator, we have...
  2. T

    Simple Harmonic Motion: Oscillator

    An oscillator with a mass of 600 g and a period of 0.50 s has an amplitude that decreased by 2.0% during each complete oscillation. If the initial amplitude is 6 cm, what will be the amplitude after 25 oscillations? I should most likely be using T = 2pi*sqrt L/g, as well as the many...
  3. C

    Solving ode of forced oscillator with dumping

    Hi i have to solve this ODE which descirbes motion of forced oscillator with dumping and constant friction :p I'm already solving it numerically with Runge-Kutta 4 yet I'm totaly puzzeled how to do it analytically. equation: mx'' + kx' + w^2_0x + F_f = A cos(\delta t) Ff delta k and...
  4. H

    SImple Harmonic Oscillator under constant friction force

    Homework Statement There is a mass attached to two springs on a table. Coefficients of static and sliding friction between the mass and table are equal with the value \mu. The particle is released at time t=0 with a positive displacement x0 from equilibrium. Given that 2kx0 > \mumg write...
  5. C

    Automotive Suspension: harmonic oscillator system, differential equations

    Homework Statement You are working at a company that designs suspension systems. Some guy from the marketing department asks you to design a shock absorber that "bounces twice", meaning that after the initial bump, the spring should expand, compress, expand again and then gradually settle...
  6. O

    Quantum Harmonic Oscillator - What is the Temperature of the system?

    Homework Statement A quantum mechanical harmonic oscillator with resonance frequency ω is placed in an environment at temperature T. Its mean excitation energy (above the ground state energy) is 0.3ħω. Determine the temperature of this system in units of its Einstein-temperature ΘE = ħω/kB...
  7. C

    Two loudspeakers, an oscillator and constructive interference at a point?

    Homework Statement Two loudspeakers placed X meters apart are driven in phase by an audio oscillator, whose frequency range is 1300 Hz to 1800 Hz. A point P is located A meters from one loudspeaker and B meters from the other. The speed of sound is 344 m/s. What is the frequency produced by...
  8. C

    Simple Harmonic Oscillator - Schrodinger Equation

    Homework Statement One possible solution for the wave function ψn for the simple harmonic oscillator is ψn = A (2*αx2 -1 ) e-αx2/2 where A is a constant. What is the value of the energy level En? Homework Equations The time independent Schrodinger wave equation d2ψ / dx2 =...
  9. S

    Phase Shift Oscillator: Why, What & How

    hi i want to know why R-C oscillator is called phase shift oscillator? does it only shift the phase?How the amplitude and the frequency of oscillator ca be changed? thanks
  10. K

    Coupled damped harmonic oscillator

    Hi everyone, I'm dealing with system identification for the first time in my life and am in desperate need of help :) The system is spring-mounted and I'm analyzing the vertical and torsional displacements. However, it seems like the vertical and torsional oscillations are coupled (shouldn't...
  11. M

    Finding Coefficients for Coupled Harmonic Oscillator

    I've been looking at a coupled harmonic oscillator, and normal modes of this: http://en.wikipedia.org/wiki/Normal_mode#Example_.E2.80.94_normal_modes_of_coupled_oscillators At the bottom of this example it says: This corresponds to the masses moving in the opposite directions, while the...
  12. H

    Question About Bloch Oscillation: Understand the Energy

    i have a question concerning BLOCH OSCILLTION.i studied that in the extended zone scheme, the energy of an electron with k=pi/d is same as with k=3 pi/d. i can't understand this because by dispersion relation as wave vector increases ,energy also increases(in extended zone scheme too) please...
  13. I

    Simple Harmonic Oscillator (time independant Schrodingers)

    Homework Statement Particle mass m is confined by a one dimensional simple harmonic oscillator potential V(x)=Cx2, where x is the displaecment from equilibrium and C is a constant By substitution into time-independant schrodingers with the potential show that \psi(x)=Axe-ax2 is a...
  14. D

    Two coupled harmonic oscillator, damping each other

    The problem is: Two damped harmonic oscillator are coupled. Both oscillators has same natural frequency \omega_0 and damping constant \beta. 1st oscillator is damped by 2nd oscillator. Damping force is proportional to velocity of 2nd oscillator. And, vice versa, 2nd oscillator is...
  15. L

    Matching Initial Position and Velocity of Oscillator

    1. Find C and S in terms of the initial position and velocity of the oscillator. Give your answers in terms of x_0, v_0, and omega. Separate your answers with a comma. 2. x(t) = X_0 + v_0*t + 0.5at^2 x(t) = C*cos(omega*t) + S*sin(omega*t) 3. Taking the derivative of x(t): v(t)...
  16. B

    Simple Harmonic Oscillator: From Hooke's Law to Harmonious Motion

    Homework Statement Show simple harmonic motion starting from Hooke's Law. The Attempt at a Solution F=-kx =m\frac{d^2x}{dt^2}=-kx \frac{1}{x}\frac{d^2x}{dt^2}=-\frac{k}{m} =\frac{1}{x}\frac{d}{dt}\frac{dx}{dt}=-\frac{k}{m}...
  17. J

    Separation of variables for quantum harmonic oscillator

    a) Show that the Hamiltonian for the quantum harmonic oscillator in 3D is separable, b) calculate the energy levels.----a) If it's separable H = H_x + H_y + H_z, so do I just re-arrange the kinetic and potential terms of the Hamiltonian in this case? that seems kind of trivial, as if I'm...
  18. B

    Charged harmonic oscillator in an electric field

    Homework Statement A charged harmonic oscillator is placed in an external electric field \epsilon i.e. its hamiltonian is H = \frac{p^2}{2m} + \frac{1}{2}m \omega ^2 x^2 - q \epsilon x Find the eigenvalues and eigenstates of energy Homework Equations The Attempt at a Solution...
  19. P

    Calculating Uncertainty in a Quantum Oscillator Mixed State

    Homework Statement Consider a quantum oscillator in a mixed state described by the density operator \rho = \frac{1}{2}( |\alpha><\alpha| + |-\alpha><-\alpha| ) . Calculate \Delta (\hat{X}^2)_1 and \Delta (\hat{X}^2)_2 in this case. Where X1 and X2 are the dimensionless position and...
  20. H

    Where to purchase a 1.7 GHz Oscillator

    Hi guys, I was just wondering of there is any companies that manufactures a 1.7 Ghz oscillators ? For the thing I need, I have a stable supply of voltage and I need a specfic frequencey, the one mentioned above. So a VCO, I think, is not the solution as some of you may suggest...
  21. D

    Designin (very simple) oscillator circuit

    I'm using the Microwave Office simulating software to design a practice clapp oscillator (picture attached). I'm at the beginning stages of this project. I will have to design a biasing network for this circuit but, before that, I need to find the formula to find the resonant frequency for...
  22. P

    Harmonic oscillator and the HUP

    Homework Statement Prove that a 1-d harmonic oscillator in ground state obeys the HUP by computing delta P sub x and delta X Homework Equations delta x = sqrt(<x^2>-<x>^2) delta px = sqrt(<px^2>-<px>^2) The Attempt at a Solution I have absolutely no idea where to start with...
  23. O

    Unusual harmonic oscillator.

    Homework Statement A particle of mass m moves (in the region x>0) under a force F = -kx + c/x, where k and c are positive constants. Find the corresponding potential energy function. Determine the position of equilibrium, and the frequency of small oscillations about it. The Attempt at a...
  24. A

    Simple Harmonic Oscillator - Normalization Constant

    Homework Statement Determine the normalization constants for the harmonic oscillator wavefunctions with v=0, and v=1 by evaluating their normalization integrals and show that they correspond to N=\frac{1}{\pi^{.5} * 2^v * v!}Homework Equations The Attempt at a Solution \int \psi^{2}d\tau=1...
  25. M

    Harmonic oscillator problem

    Homework Statement A particle with with the mass of m is attached to a spring (with no mass, spring constant k, length l) which is attached to a wall. The particle is moving with no friction along the x-axis. a) Write the particles motion equation, and find the general solution to the motion...
  26. N

    Wave function of a simple harmonic oscillator

    Homework Statement The ground state wave function of a one-dimensional simple harmonic oscillator is \varphi_0(x) \propto e^(-x^2/x_0^2), where x_0 is a constant. Given that the wave function of this system at a fixed instant of time is \phi\phi \propto e^(-x^2/y^2) where y is another...
  27. D

    Simple Harmonic Oscillator Troubles

    Homework Statement This is a 3 part problem, mass M on a spring of length l with mass m. The first part was to derive the Kinetic Energy of one segment dy, second part was to Integrate this and get the Kinetic Energy of (1/6)m(V^2) where V is the velocity of the Mass M at the end of the...
  28. C

    Eigenvalues/functions for hamiltonian in 1D harmonic oscillator

    Homework Statement Find the eigenvalues and eigenfunctions of H\hat{} for a 1D harmonic oscillator system with V(x) = infinity for x<0, V(x) = 1/2kx^2 for x > or equal to 0. Homework Equations The Attempt at a Solution I think the hamiltonian is equal to the potential + kinetic...
  29. W

    Hydrogen molecule as harmonic oscillator

    Homework Statement The harmonic oscillator problem may be used to describe the vibrations of molecules. For example, the hydrogen molecule H2 is found to have equally spaced vibrational energy levels separated by 8.7 × 10-20 J. What value of the force constant of the spring would be needed to...
  30. W

    Energy quantization of oscillator

    Homework Statement A simple pendulum has a length equal to 0.6 m and has a bob that has a mass equal to 0.5 kg. The energy of this oscillator is quantized, and the allowed values of energy are given by En = (n + 1/2)hf0, where n is an integer and f0 is the frequency of the pendulum. Find n if...
  31. A

    What is that oscillator type?

    what is that oscillator type?
  32. J

    State of Harmonic Oscillator with spin half

    Homework Statement The state of Harmonic Oscillator with spin half is |\psi>=\frac{1}{\sqrt{2}}( |n=0,\uparrow> + |n=1, \downarrow>) a, say which one is the possible outcome for a measure of ^{^}S_{x} and find the probability of measuring each possible outcome. b, find the state of the...
  33. B

    Quantum Harmonic Oscillator: Negative Kinetic Energy Question.

    Hello everybody, I noticed these questions are lengthy. If you want to skip my introduction, just scroll down to the questions. I put *** next to each one. I just started Quantum Theory I this semester and I have a question (actually two questions) regarding the quantum harmonic...
  34. E

    How Does the Driven Oscillator ODE Describe Long-Term Motion?

    Homework Statement "The equation mx'' + kx = F0 * Sin (wt) governs the motion of an undamped harmonic oscillator driven by a sinusoidal force of angular frequency w. Show that the steady-state solution is x = F0 * Sin (wt) /(m * (w0^2 - w^2)) Homework Equations x(t) = xta(t) +...
  35. K

    Quantum harmonic oscillator minimum energy

    http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hosc4.html#c1 I know the energy should be E = \frac{{{p^2}}}{{2m}} + \frac{1}{2}m{\omega ^2}{x^2} But I can't figure out why the minimum energy is related to \Delta p
  36. S

    What Is the Relationship Between Damping and Resonance in Driven Oscillators?

    Homework Statement A driven oscillator with mass m, spring constant k, and damping coefficient b is is driven by a force F_{o}cos(\omega t). The resulting steady-state oscillations are described by x(t) = Re{\underline{A}e^{i\omega t}} where: \underline{A} = \frac{F_{0}/m}{(\omega_{o}^{2} -...
  37. E

    Damped harmonic oscillator and displacement

    Homework Statement "Show that the ratio of two successive maxima in the displacement of a damped harmonic oscillator is constant."Homework Equations x = a e^(-\upsilont/2) cos (\omegat - \vartheta)The Attempt at a Solution So I want to find when this beast has its maximum values, so I take the...
  38. R

    Average energy of a harmonic oscillator

    Hello PF members, Is there some good book, which contain the derivation of average energy of a harmonic oscillator at temperature T. I want to derive from Planck's distribution (PD) function (<n>=(exp(##\hbar\omega/kT##)-1)##^{-1}##)...to get the following relation: energy E=...
  39. M

    Old Quantum Theory and the Linear Harmonic Oscillator

    Homework Statement Calculate the quantized energy levels of a linear harmonic oscillator of angular frequency $\omega$ in the old quantum theory. Homework Equations \[ \oint p_i dq_i = n h \] The Attempt at a Solution This is supposed to be a simple "exercise" (the first in...
  40. N

    Hamiltonian problem concerning the simple harmonic oscillator

    Homework Statement use the hamiltonian equation H=H_x+H_y+H_z to show that wave functions of the form \varphi(r)=\phii(x)\phij(y)\phik(z) where the functions phi_i(x) are the energy eigenfunctions for a 1-d SHM , satisfy H*phi=E*phi , and find the followed values of E for the 3-d...
  41. H

    Where can I get a 2.45 GHz Oscillator

    Hi Guys, Where can I find a 2.45 GHz oscillator, ready made ? thanks in advance
  42. A

    Solving Schrödinger Eq. for Harmonic Oscillator

    Homework Statement I wonder if someone could help me to arrive at equation 2.56 by performing the substitutions. Please see the attachment Homework Equations Please see the attachment for this part. and also for the attempt of a solution.
  43. I

    How Long Does It Take for a Damped Oscillator's Energy to Halve?

    Homework Statement A mass M is suspended from a spring and oscillates with a period of 0.880 s. Each complete oscillation results in an amplitude reduction of a factor of 0.96 due to a small velocity dependent frictional effect. Calculate the time it takes for the total energy of the...
  44. C

    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...
  45. T

    Griffiths' QM book: series solution to harmonic oscillator

    I'm trying to read through Griffiths' QM book, and right now I'm on the series solution to the harmonic oscillator (ch 2). I'm having a hard time following the math (especially after equation 2.81) in this section, so if anyone has read this book, please help. My first question is about the...
  46. S

    555 Oscillator Frequency Fluctuating Rapidly

    hey all, I've wired up a standard 555 timer, using two resistors, a capacitor and a diode to make a clock in order to feed a stepper motor controller. http://wolfstone.halloweenhost.com/TechBase/com555_555AnyDutyCycle.gif Its wired like the schematic above. My resistor values are the...
  47. M

    The Energy Levels of a Quantum Harmonic Oscillator

    I've followed this: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hosc3.html#c1, up to the part where it gets to here: . The guide says: "Then setting the constant terms equal gives the energy"? Am I being stupid? I really can't see where that equations come from.
  48. R

    Exploring the Solution to a Harmonic Oscillator Problem

    I am not really asking how to solve the problem but just for explanation of what I know to be true from the problems solution. Basically the original problem statement is this: A particle in a harmonic oscillator potential starts out in the state |psi(x,0)>=1/5 * [3|0> + 4|1>] and it asks to...
  49. O

    Understanding the Wien Bridge Oscillator Circuit

    Hi all, I am doing a project on electronics about the Wien Bridge Oscillator. I learned about impedances and operational amplifiers and now I'm trying to understand the Wien Bridge circuit. I'm having some problems understanding it and I would be very happy to get some help. I still have not...
  50. H

    Designing a 2.455 GHz Oscillator

    Hi All, I would really like your help in my design project, which is about desgining, as mentioned in the title, an oscillator with 2.455 GHz frequencey. I want it to be efficent to the greatest extent, meaning the lowest power consumption possible and greatest stablitiy. I'm confused...
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