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. renec112

    Harmonic oscillator - chance of of finding particle x>0

    Homework Statement A particle is moving in a 1-dimensional harmonic osciallator with the hamiltion: ## H = \hbar \omega (a_+ a_- + \frac{1}{2})## at time ## t=0## the normalized wave function is given by ## \Psi(x,0) = \frac{1}{\sqrt{2}}(\psi_0(x) + i\psi_1(x)) ## Task: Calculate for ## t \geq...
  2. renec112

    QM: expectation value and variance of harmonic oscillator

    Homework Statement A particle is moving in a one-dimensional harmonic oscillator, described by the Hamilton operator: H = \hbar \omega (a_+ a_- + \frac{1}{2}) at t = 0 we have \Psi(x,0) = \frac{1}{\sqrt{2}}(\psi_0(x)+i\psi_1(x)) Find the expectation value and variance of harmonic oscillator...
  3. E

    How can we double the amplitude of an oscillator?

    Homework Statement The amplitude of any oscillator can be doubled by: A. doubling only the initial displacement B. doubling only the initial speed C. doubling the initial displacement and halving the initial speed D. doubling the initial speed and halving the initial displacement E. doubling...
  4. cromata

    I Boundary conditions of a forced oscillator (string)

    -If we have string of length L that has fixed ends, then we can easily find frequencies with which this string can oscillate: We just need to solve wave equation: ∂2y/∂x2=1/c2*∂2∂t2 (c is determined by strings properties (linear density and tension), with Dirichlet boundary conditions...
  5. B

    Damped driven oscillator

    Homework Statement I have a project in university that's about creating a simplified model of a washing machine in the program ADAMs View. Here is a picture of how it's constructed: https://imgur.com/a/zZzS5 So basically to oversimplify the problem I've understood that the rotating mass will...
  6. S

    Griffith's QM, Harmonic Oscillator approximate solution eq

    Homework Statement on page 51 (of my book, probably not current) section 2.3.2 equation 2.74 and 2.75 d2ψ / dξ2 ≈ ψξ2 Homework Equations This is an approximation of the Schrodinger equation with a variable introduced ξ = √(mω/h) The solution is given: ψ(ξ) = Ae-ξ2/2 +Beξ2/2The Attempt at...
  7. V

    Exponentially driven harmonic oscillator

    Homework Statement An un-damped harmonic oscillator natural frequency ##\omega_0## is subjected to a driving force, $$F(t)=ame^{-bt}.$$ At time, ##t=0##, ##x=\dot{x}=0##. Find the equation of motion. Homework Equations ##F=m\ddot{x}## The Attempt at a Solution We have...
  8. G

    Relativistic Harmonic Oscillator Lagrangian and Four Force

    Homework Statement Consider an inertial laboratory frame S with coordinates (##\lambda##; ##x##). The Lagrangian for the relativistic harmonic oscillator in that frame is given by ##L =-mc\sqrt{\dot x^{\mu} \dot x_{\mu}} -\frac {1}{2} k(\Delta x)^2 \frac{\dot x^{0}}{c}## where ##x^0...
  9. G

    I Relativistic harmonic oscillator

    I have some difficulties in viewing the literature on the topic. In textbooks on analytical mechnics the procedure given for Special relativistic motion is to write the kinetic term relativistically and attach the unchanged potential term. So, for a harmonic oscillator the Lagrangian is ##L =...
  10. tarkin

    QM harmonic oscillator - integrating over a gaussian?

    Homework Statement [/B] For the first excited state of a Q.H.O., what is the probability of finding the particle in -0.2 < x < 0.2 Homework Equations Wavefunction for first excited state: Ψ= (√2) y e-y2/2 where: The Attempt at a Solution To find the probability, I tried the integral of...
  11. A

    B Relativistic Spring-Mass Oscillator: A Paradox?

    Consider a spring-mass oscillator on a train moving at relativistic speed. According to SR, to a stationary observer, both the mass and the period will appear to have increased by a factor of γ. But the period is supposed to be proportional to the square root of the mass. Something is wrong...
  12. S

    Recurrence relation for harmonic oscillator wave functions

    1. Homework Statement I've been using a recurrence relation from "Adv. in Physics"1966 Nr.57 Vol 15 . The relation is : where Rnl are radial harmonic oscillator wave functions of form: The problem is that I can't prove the relation above with the form of Rnl given by the author(above). I've...
  13. F

    I How does a harmonic oscillator model have the same frequency

    I'm currently studying IR but my mind is having trouble tying everything together. While I see that vibrational frequency is determined really by just reduced mass, I can see from the equation that vib equation is the same throughout energy levels and so does energy (bc that basically depends...
  14. Luxucs

    Normal force as a function of time (oscillator)

    Homework Statement A spring with spring constant k is attached to a box of mass M in which is placed a small body of mass m. The system is displaced a distance A from equilibrium and released from rest. Find the normal force between the box and the small mass as a function of time. For what...
  15. F

    Harmonic Oscillator with Friction

    Homework Statement I don’t have a specific problem to solve, and I’m not sure I would be able to correctly find one, but I need to know how to solve a harmonic Oscilator problem with Friction. I believe I should be starting with F = -kx -Ff, and that I will be given some information about the...
  16. O

    Equation of motion in harmonic oscillator hamiltonian

    See attached photo please. So, I don't get how equations of motion derived. Why is it that x dot is partial derivative of H in term of p but p dot is negative partial derivative of H in term of x.
  17. N

    Virial Theorem and Simple Harmonic Oscillator

    Homework Statement Show that the virial theorem holds for all harmonic-oscillator states. The identity given in problem 5-10 is helpful. Homework Equations Identity given: ∫ξ2H2n(ξ)e-ξ2dξ = 2nn!(n+1/2)√pi P.S the ξ in the exponent should be raised to the 2nd power. So it should look like ξ2...
  18. N

    Lowering Operator Simple Harmonic Oscillator n=3

    Homework Statement Show that application of the lowering Operator A- to the n=3 harmonic oscillator wavefunction leads to the result predicted by Equation (5.6.22). Homework Equations Equation (5.6.22): A-Ψn = -iΨn-1√n The Attempt at a Solution I began by saying what the answer should end...
  19. G

    Understanding single transistor oscillator

    I see this circuit has many applications for creating high voltage from a battery source in a very simple and compact manner. However, I’m not sure of the exact basis of oscillation - is it: 1. Current flows through FB, turns on transistor. 2. Primary induces opposing voltage in FB due to...
  20. Muthumanimaran

    Particle in one-dimensional harmonic oscillator

    Homework Statement This is a question asked in a entrance examination[/B] A charged particle is in the ground state of a one-dimensional harmonic oscillator potential, generated by electrical means. If the power is suddenly switched off, so that the potential disappears, then, according to...
  21. W

    Complex Solutions to Oscillations

    Homework Statement Homework EquationsThe Attempt at a Solution I tried differentiating both sides of 3 and re-arranging it such that it started to look like equation 2, however i got stuck with 2 first order terms z' and couldn't find a way to manipulate it into a function z. I then tried...
  22. JTC

    I Meaning of the word "Harmonic" in different contexts

    A harmonic function is one that satisfies Laplace's equation -- a definition cannot be more precise than that. However, in the study of vibrations, sine and cosine are considered harmonic functions; but they don't solve Laplace's equation. And then there are words like: harmonics (for higher...
  23. Gh. Soleimani

    A The differential equation of Damped Harmonic Oscillator

    If you consider b^2/m > 4*k, you can get the solution by using classic method (b = damping constant, m = mass and k = spring constant) otherwise you have to use complex numbers. How have the references books proved the solution for this differential equation?
  24. R

    Can an undamped harmonic oscillator have a steady-state solution?

    Homework Statement An undamped harmonic oscillator (b=0) is subject to an applied force Focos(wt). Show that if w=wo, there is no steady- state solution. Find a particular solution by starting with a solution for w=wo+#, and passing to the limit #->0, it will blow up. Try starting with a...
  25. PainterGuy

    I Atom as a harmonic oscillator of radition

    Hi Q1: I was reading about ultraviolet catastrophe and it was said that atoms were assumed to be harmonic oscillators of radiation. I believe that two harmonic oscillators could have the same frequency but different amplitudes so it would mean that two different atoms (i.e. two harmonic...
  26. JTC

    A Where Can I Find a Tutorial Animation for Damping of a 1D Oscillator?

    (I list this as Advanced because the question is not what it seems from the title.) So most know the cases: no damping, underdamping, critical damping, overdamping. I got that: this is not a request for explanation. Rather... Does anyone know of a web page that has some tutorial ANIMATION...
  27. N

    A Driven Harmonic Oscillator where Mass Hits Ground

    I started to ponder following problem. I have a driven, damped oscillator where the mass is free to vibrate in y-direction. If I put a wall or a ground near the mass, the mass touches it if the drive amplitude is larger than the distance to the ground. How does this change the normal dynamics. I...
  28. D

    I How is the CSCO in an harmonic oscillator?

    Hi everyone, I have a great doubt in this problem: Let a mass m with spin 1/2, subject to the following central potencial V(r): V(r)=1/2mω2r2 Find the constants of motion and the CSCO to solve the Hamiltonian? This is my doubt, I can't find the CSCO in this potencial. Is a problem in general...
  29. Tspirit

    The plots of wave function of harmonic oscillator

    Homework Statement In Griffiths' book "Introduction to Quantum Mechanics", Section 2.3, Chapter 2, the Fig. 2.7 gives the plots of the wave function (##\psi_{n}##) and its modulus of the harmonics oscillator, see the Appendix. With the order (##n##) increasing, they become both higher. However...
  30. JulienB

    3D quantum harmonic oscillator: linear combination of states

    Homework Statement Hi everybody! In my quantum mechanics introductory course we were given an exercise about the 3D quantum harmonic oscillator. We are supposed to write the state ##l=2##, ##m=2## with energy ##E=\frac{7}{2}\hbar \omega## as a linear combination of Cartesian states...
  31. binbagsss

    Statistical Mechanics: Canonical Partition Function & Anharmonic Oscillator

    Homework Statement With the Hamiltonian here: Compute the cananonical ensemble partition function given by ##\frac{1}{h} \int dq dp \exp^{-\beta(H(p,q)}## for 1-d , where ##h## is planks constant Homework EquationsThe Attempt at a Solution I am okay for the ##p^2/2m## term and the...
  32. B

    Commutation Relations, 2D Harmonic Oscillator

    Homework Statement Consider a two-dimensional harmonic oscillator, described by the Hamiltonian ##\hat H_0 = \hbar \omega (\hat a_x \hat a_x ^{\dagger} + \hat a_y \hat a_y^{\dagger} + 1)## Calculate ##\hat H_0 \hat L | n_1, n_2 \rangle## and ##\hat L \hat H_0 |n_1, n_2 \rangle##. What does...
  33. alex91alex91alex

    Harmonic Oscillator Homework: Issues with d)

    Homework Statement I am having issues with d) and would like to know if I did the a, b, and c correctly. I have tried to look online for explanation but with no success. A harmonic oscillator executes motion according to the equation x=(12.4cm)cos( (34.4 rad /s)t+ π/5 ) . a) Determine the...
  34. TheBigDig

    Acceleration amplitude of a damped harmonic oscillator

    Homework Statement The acceleration amplitude of a damped harmonic oscillator is given by $$A_{acc}(\omega) = \frac{QF_o}{m} \frac{\omega}{\omega _o} \sqrt{\it{R}(\omega)}$$ Show that as ##\lim_{\omega\to\infty}, A_{acc}(\omega) = \frac{F_o}{m}## Homework Equations $$\it{R}(\omega) =...
  35. R

    Simple Harmonic Oscillator behaviour when a potential term is added

    Homework Statement A simple harmonic oscillator has a potential energy V=1/2 kx^2. An additional potential term V = ax is added then, a) It is SHM with decreased frequency around a shifted equilibrium b) Motion is no longer SHM c)It is SHM with decreased frequency around a shifted equilibrium...
  36. AHMEDbr

    Designing a 150MHz Clapp Oscillator with 0.24u Inductance for Your Project

    hi , i want to design a clapp oscillator with output frequency up to 150 MHZ , inductance value must be 0.24 u , who can help me please?? i need it for my project
  37. Vitani11

    Overdamped oscillator solution as hyperbolic function?

    Homework Statement Here is the equation for the general solution of an overdamped harmonic oscillator: x(t) = e-βt(C1eωt+C2e-ωt) Homework Equations β decay constant C1, C2 constants ω frequency t time The Attempt at a Solution I know (eωt+e-ωt)/2 = coshωt and (eωt-e-ωt)/2 = sinhωt but how do...
  38. B

    Average energy of a damped driven oscillator

    Homework Statement http://imgur.com/a/lv6Uo Homework Equations Look below The Attempt at a Solution I was unsure where to start. I thought that parseval's theorem may be helpful. I know the Potential energy is equivalent to .5kx^2 and T will be the integral of the force. So i have $$<E> =...
  39. V

    Linear perturbation to harmonic oscillator

    Homework Statement Find the first-order corrections to energy and the wavefunction, for a 1D harmonic oscillator which is linearly perturbed by ##H'=ax##. Homework Equations First-order correction to the energy is given by, ##E^{(1)}=\langle n|H'|n\rangle##, while first-order correction to the...
  40. V

    Anharmonic oscillator first-order correction to energy

    Homework Statement I have ##H'=ax^3+bx^4##, and wish to find the general perturbed wave-functions. Homework Equations First-order correction to the wave-function is given by, $$\psi_n^{(1)}=\Sigma_{m\neq n}\frac{\langle\psi_m^{(0)}|H'|\psi_n^{(0)}\rangle}{n-m}|\psi_m^{(0)}\rangle.$$ The...
  41. H

    A Uncertainty Propagation in Coupled Oscillator

    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...
  42. M

    Quantum Oscillator with different frequencies

    Homework Statement Solve the Schrödinger Equation for an harmonic potential of the form (1/2)m\omega_+^2x^2 for x>0 and (1/2)m\omega_-^2x^2 for x<0. Find the equation that determines the energy spectrum. You can use m=1/2 and \hbar=1 Homework Equations [/B] I wrote down Schrödinger Equation...
  43. Crush1986

    Quantum Harmonic Oscillator Problem

    Homework Statement Substitute \psi = Ne^{-ax^2} into the position-space energy eigenvalue equation and determine the value of the constant a that makes this function an eigenfunction. What is the corresponding energy eigenvalue? Homework Equations \frac{-\hbar^2}{2m}...
  44. Adolfo Scheidt

    I Harmonic Oscillator equivalence

    Hello, I'm studying the section 2.2 of "Introduction to Quantum Mechanics, 2nd edition" (Griffiths), and he shows this equation $$\frac{\partial^2\psi}{\partial x^2} = -k^2\psi , $$ where psi is a function only of x (this equation was derivated from the time-independent Schrödinger equation) and...
  45. J

    Diagonalize a coupled damped driven oscillator

    Homework Statement I am trying to follow a paper, https://arxiv.org/pdf/1410.0710v1.pdf, I want to get the results obtained in equations 5 and 6 but can't quite work out how eq 3 has been diagonalized. Homework Equations eq 3 The Attempt at a Solution As the system is driven i thought I'd...
  46. kubaanglin

    Harmonic Oscillator- Is this correct?

    Homework Statement [/B] What is the shortest time required for a harmonic oscillator to move from ##x = A## to ##x = \frac{A}{2}##? Express your answer in terms of the period ##T##. Homework Equations [/B] ##x(t)=Acos(\omega t)=Acos(2\pi\frac{t}{T})## The Attempt at a Solution ##A=Acos(0)##...
  47. J

    Harmonic oscillator with 3 charged particles

    Homework Statement I got an alpha particle (charge 2+) fixed at x=0 and an electron fixed at x=2. I then add a fluor ion (charge 1-) to the right of the electron and we note his position xeq. The question is to find the constant spring (k) relative to the harmonic oscillation made by the fluor...
  48. genxium

    Does Wien bridge oscillator have a closed-loop gain?

    Homework Statement By Wien bridge oscillator (abbreviated as WBO below) I refer to this circuit where the op-amp is assumed to be ideal and the output is the voltage drained from the upper end of R3. What confuses me is that I hardly find a reference which explicitly states that a WBO has a...
  49. L

    The Minimum voltage requirement for an RC Oscillator

    Hi I am trying to run an RC oscillator using a 2N3904 (Datasheet for reference: http://www.kynix.com/uploadfiles/pdf8798/2N3904.pdf) The circuit looks like the following. I want to run it at 0-5v but I failed, I assume it is because the voltage is not high enough? What would you expect the...
  50. P

    Feedback needed for an oscillator or multivibrator

    i want to ask why the feed back at multivibrator must be positive feedback ?
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