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. Helena Wells

    Should a Big Inductor be Added to a Hartley Oscillator Design?

    This is the Colpitts oscillator: When we design a Colpitts oscillator we must set the value of C1 to be bigger than the parasitic capacitance of the emitter base junction. However in a Hartley oscillator we have an inductive voltage divider and I was wondering if we should put a big inductor...
  2. aiyiaiyiai

    Mass-spring oscillator problem

    I understand the masses will accelerate toward each other with the same varying speed before they reach the natural length of the spring. Then they continue to approach each other while compress the spring, that'll slow their speeds down definitely. So my question is, how could we calculate how...
  3. Q

    Harmonic Oscillator With and Without Friction (mass on a spring)

  4. J

    I Zero-point energy of the harmonic oscillator

    First time posting in this part of the website, I apologize in advance if my formatting is off. This isn't quite a homework question so much as me trying to reason through the work in a way that quickly makes sense in my head. I am posting in hopes that someone can tell me if my reasoning is...
  5. Leo Liu

    A piece of clay stuck to a SHM oscillator

    I don't get why the total mechanical energy is not conserved in this situation. When the length of the spring reaches the maximum, the speed of the block is 0 and we have the following equation: $$E=K+U=1/2mv^2+1/2kA^2,\text{where A is the amplitude} \implies E=1/2kx_{max}^2$$ I can't see why...
  6. M

    Fermions, Bosons, and nonidentical particles in a 1-d oscillator

    I'm having a hard time understanding how to treat fermions, bosons, and distinguishable particles differently for this problem. To the best of my understanding, I know that my overall state for bosons must be symmetric, and because they're spin-0, this means there's only one coupled spin state...
  7. Lo Scrondo

    I Different invariant tori in the case of a 2D harmonic oscillator

    Hi everyone! Both sources I'm currently reading (page 291 of Mathematical Methods of Classical Mechanics by Arnol'd - get it here - and page 202 of Classical Mechanics by Shapiro - here) say that, in the case of the planar harmonic oscillator, using polar or cartesian coordinate systems leads...
  8. patric44

    The Harmonic Oscillator Asymptotic solution?

    hi guys i am trying to solve the Asymptotic differential equation of the Quantum Harmonic oscillator using power series method and i am kinda stuck : $$y'' = (x^{2}-ε)y$$ the asymptotic equation becomes : $$y'' ≈ x^{2}y$$ using the power series method ##y(x) = \sum_{0}^{∞} a_{n}x^{n}## , this...
  9. chocopanda

    Harmonic oscillator with ladder operators - proof using the Sum Rule

    I'm trying verify the proof of the sum rule for the one-dimensional harmonic oscillator: $$\sum_l^\infty (E_l-E_n)\ | \langle l \ |p| \ n \rangle |^2 = \frac {mh^2w^2}{2} $$ The exercise explicitly says to use laddle operators and to express $p$ with $$b=\sqrt{\frac {mw}{2 \hbar}}-\frac...
  10. Mayan Fung

    Perturbation from a quantum harmonic oscillator potential

    For the off-diagonal term, it is obvious that (p^2+q^2) returns 0 in the integration (##<m|p^2+q^2|n> = E<m|n> = 0##). However, (pq+qp) seems to give a complicated expression because of the complicated wavefunctions of a quantum harmonic oscillator. I wonder whether there is a good method to...
  11. VVS2000

    Time period of a harmonic oscillator

  12. cianfa72

    Accounting for mutual inductance in a Hartley Oscillator

    Hi, I'm watching a video about Hartley oscillator and I'm in trouble with a simple assumption: as stated at minute 5:50 if the two coils ##L_1## and ##L_2## are wound on the same core then taking into account the mutual inductance M he gets: ##L^ {'} _1 = L_1 + M## ##L^ {'} _2 = L_2 + M##...
  13. K

    A Equipartition theorem and Coupled harmonic oscillator system

    Dear all, While simulating a coupled harmonic oscillator system, I encountered some puzzling results which I haven't been able to resolve. I was wondering if there is bug in my simulation or if I am interpreting results incorrectly. 1) In first case, take a simple harmonic oscillator system...
  14. Abdullah Almosalami

    Intuitive Explanation of Mass-on-Spring Oscillator Frequency

    I just noticed something that is a little bit of a different perspective on a mass-on-spring (horizontal) simple (so undamped) oscillator's frequency and looking for some intuition on it. There are many ways to derive that for a mass on a horizontal frictionless surface on a spring with spring...
  15. LCSphysicist

    Graphical Analysis of damped oscillator

    First of all, i tried to find w, the angular frequency, by calculating the oscillations from ta to tc, there is ~ 20 oscillations coursed. so, w = 2*pi*20/(tc-ta) ta = 0, tc = 0 + 5.2 ms And tried to find the factor gama y by A(t) = A*cos(Φ + wt)*e^(-yt/2) A(0) = 2.75u = A*cos(Φ) 1u = A*cos(Φ...
  16. S

    Calculating degeneracy of the energy levels of a 2D harmonic oscillator

    Too dim for this kind of combinatorics. Could anyone refer me to/ explain a general way of approaching these without having to think :D. Thanks.
  17. I

    Griffiths Problem 3.35. Harmonic Oscillator, Bra-ket notation

    Firstly, apologies for the latex as the preview option is not working for me. I will fix mistakes after posting. So for ##<x>## = (##\sqrt{\frac{\hbar}{2m\omega}}##) ##(< \alpha | a_{+} + a_{-}| \alpha >)## = (##\sqrt{\frac{\hbar}{2m\omega}}##) ##< a_{-} \alpha | \alpha> + <\alpha | a_{-}...
  18. handyman123

    Not able to get the desired output frequency using a Wein Bridge Oscillator

    Can anyone help me find what is wrong in this circuit? given, slew rate of the op amp is 400V/us and max output current for opamp is 40mA but the opamp is lm741.
  19. S

    What happens to the c2sin(t) part of the worked solution?

    Hello folks, So the solution of the equation of motion for damped oscillation is as stated above. If we were to take an specific example such as: $$\frac{d^2x}{dt^2}+4\frac{dx}{dt}+5x=0$$ then the worked solution to the second order homogeneous is...
  20. VapeL

    Equation of motion and normal modes of a coupled oscillator

    This is a question from an exercise I don't have the answers to. I have been trying to figure this out for a long time and don't know what to do after writing mx''¨(t)=−kx(t)+mg I figure that the frequency ω=√(k/m) since the mg term is constant and the kx term is the only term that changes. I...
  21. Lo Scrondo

    I Time averages for a 2-dimensional harmonic oscillator

    I'm studying Ergodic Theory and I think I "got" the concept, but I need an example to verify it... Let's take the simplest possible 2D classical harmonic oscillator whose kinetic energy is $$T=\frac{\dot x^2}{2}+\frac{\dot y^2}{2}$$ and potential energy is $$U=\frac{ x^2}{2}+\frac{y^2}{2}$$...
  22. D

    Phase space of a harmonic oscillator and a pendulum

    Hello everybody, new here. Sorry in advance if I didn't follow a specific guideline to ask this. Anyways, I've got as a homework assignment two cannonical transformations (q,p)-->(Q,P). I have to obtain the hamiltonian of a harmonic oscillator, and then the new coordinates and the hamiltonian...
  23. S

    Normalization constant A of a harmonic oscillator

    I've worked through it doing what I thought I should have done. I normalized the original wavefunction(x,0) and made it = one before using orthonormality to get to A^2(1-1) because i^2=-1 but my final answer comes out at 1/0 which is undefined and I don't see how that could be correct since A is...
  24. C

    Electrical Building a Kilohertz Oscillator: Tips and Tricks

    Now, I once read in another thread here someone else was trying to make a kilohertz oscillator. The forum members said not to use a breadboard as it would create too much noise. So What do you recommend as an alternative? Or should I just connect the components without the foundation? Also...
  25. T

    Op-amp Oscillator Circuit Design (10-50 MHz)

    Questions: 1. Is LM741 capable of oscillating at 10MHz? If not, could you suggest me an affordable op-amp for this operation? 2. How likely am I, as a beginner to be able to design a zero phase shift feedback filter to use with a non-inverting op-amp circuit to create an oscillator? 3. If an...
  26. J

    I Atoms in a harmonic oscillator and number states

    I am confused about the relation between the number state ##|n\rangle## with the annhilation and creation operators ##a^\dagger## and ##a## respectively, and the number of atoms in the harmonic oscillator. I'll try to express my current understanding, I thought the number states represent the...
  27. JD_PM

    Working out harmonic oscillator operators at ##L \rightarrow \infty##

    Let's go step by step a) We know that the harmonic oscillator operators are $$a^{\dagger} = \frac{1}{\sqrt{2 \hbar m \omega}} ( -ip + m \omega q)$$ $$a= \frac{1}{\sqrt{2 \hbar m \omega}} (ip + m \omega q)$$ But these do not depend on ##L##, so I guess these are not the expressions we want...
  28. Tony Hau

    Angular frequency of a damped oscillator

    So in my textbook on oscillations, it says that angular frequency can be defined for a damped oscillator. The formula is given by: Angular Frequency = 2π/(2T), where T is the time between adjacent zero x-axis crossings. In this case, the angular frequency has meaning for a given time period...
  29. JD_PM

    A Understanding Cartan subalgebra applied to the n-harmonic oscillator

    I was studying the ##n##-dimensional harmonic oscillator, whose Hamiltonian is $$\hat H = \sum_{j=1}^{n} \Big( \frac{1}{2m} \hat p_j^2 + \frac{\omega^2 m}{2} \hat q_j^2 \Big)$$ The ladder operators are $$a_{\pm} = \frac{1}{\sqrt{2 \hbar m \omega}} ( \mp ip + m \omega q)$$ And came across an...
  30. A

    A Piezoelectricity and the Lorentz Harmonic Oscillator?

    Hi! As I outlined in my https://www.physicsforums.com/threads/hello-reality-anyone-familiar-with-the-davisson-germer-experiment.985063/post-6305937, I'm curious to ask if there is anyone with knowledge on the theory of the piezoelectric effect on this forum? I think it's fascinating how a...
  31. M

    A critically damped simple harmonic oscillator - Find Friction

    c = Critically Damped factor c = 2√(km) c = 2 × √(150 × .58) = 18.65 Friction force = -cv Velocity v = disp/time = .05/3.5 Friction force = - 18.65 * .05/3.5 = -.27 N I am not sure if above is correct. Please check and let me know how to do it.
  32. Quentief

    The Poulcen Arc: Exploring the First Electric Oscillator

    Hi everyone 🙂 I have read this article about the arc converter, also known as the Poulcen arc. https://en.m.wikipedia.org/wiki/Arc_converter It was apparently one of the first electric oscillators. Apparently, an electric arc was produced between two electrodes to put in resonance a RLC...
  33. G

    Harmonic Oscillator Ladder Operators - What is (ahat_+)^+?

    I know that ahat_+ = 1/sqrt((2*m*h_bar*w)) * (mw(xhat)+i(phat)) and ahat_- = 1/sqrt((2*m*h_bar*w)) * (mw(xhat)-i(phat)). But I'm not sure what (ahat_+)^+ could be.
  34. P

    Damped Oscillator and Oscillatory Driving Force

    I found the steady state solution as F_0(mw_0^2 - w^2m)Coswt/(mwy)^2 + (mw_0^2 -w^2m)^2 + F_0mwySinwt/(mwy)^2 + (mw_0^2 -w^2m)^2 But I'm not sure how to sketch the amplitude and phase? Do I need any extra equations?
  35. D

    A Understanding Harmonic oscillator conventions

    I don't quite understand how he got the line below. By using discrete time approximation, we can get the second order time expression. But i don't see how by combining terms he is able to get such expression.
  36. E

    Help with the phase of the solution for a driven oscillator

    My question also applies to the damped driven oscillator, however for simplicity I will first consider an undamped oscillator. The equation of motion is $$-kx + F_{0} \cos{\omega t} = m \ddot{x}$$ or in a more convenient form $$\ddot{x} + {\omega_{0}} ^{2}x = \frac{F_{0}}{m} \cos{\omega t}$$The...
  37. T

    Simple Harmonic Oscillator Squeezing

    I'm working through https://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-fall-2013/lecture-notes/MIT8_05F13_Chap_06.pdf, and I'm stumped how they got from Equation 5.26 (##\vert 0_{\gamma} \rangle \equiv \frac{1}{\sqrt{cosh\gamma}} exp(-\frac{1}{2}tanh\gamma \hat{a^\dagger}\hat{a^\dagger}...
  38. I

    Time Derivatives of Expectation Value of X^2 in a Harmonic Oscillator

    I can show that ##\frac{d}{dt} \langle \psi (t) \vert X^2 \vert \psi (t) \rangle = \frac{1}{m} \langle \psi (t) \vert PX+XP \vert \psi (t) \rangle##. Taking another derivative with respect to time of this, I get ##\frac{d^2}{dt^2} \langle \psi (t) \vert X^2 \vert \psi (t) \rangle = \frac{i}{m...
  39. Diracobama2181

    A Volume Element for Isotropic Harmonic oscillator

    I am currently having trouble deriving the volume element for the first octant of an isotropic 3D harmonic oscillator. I know the answer I should get is $$dV=\frac{1}{2}k^{2}dk$$. What I currently have is $$dxdydz=dV$$ and $$k=x+y+z. But from that point on, I'm stuck. Any hints or reference...
  40. Diracobama2181

    A Time Dependent Perturbation of Harmonic Oscillator

    An electric field E(t) (such that E(t) → 0 fast enough as t → −∞) is incident on a charged (q) harmonic oscillator (ω) in the x direction, which gives rise to an added ”potential energy” V (x, t) = −qxE(t). This whole problem is one-dimensional. (a) Using first-order time dependent perturbation...
  41. J

    Royer Oscillator Working Principle

    Hi, I am studying Wireless Energy Transfer and I find Royer Oscillator in that. Ref: Wikipedia https://en.wikipedia.org/wiki/Royer_oscillator I am unable to understand how it works. I found a diagram here: Ref: https://www.smps.us/inverters.html It says that (quoted from webstie): In practice...
  42. P

    I Solving a quantum harmonic oscillator using quasi momentum

    In the paper below I've seen a new method to solve the quantum harmonic oscillator Introduction to the Spectrum of N=4 SYM and the Quantum Spectral Curve It is done using the concept of quasi momentum defined as $$p = - i \frac{d(\log \psi)}{dx}$$ See pg 7,8 Is this well know? is it discussed...
  43. M

    MATLAB No damping but the solution to simple harmonic oscillator damps?

    I posted yesterday but figured it out; however, a different issue I just detected with the same code arose: namely, why does the solution damp here for an undamped simple harmonic oscillator? I know the exact solution is ##\cos (5\sqrt 2 t)##. global delta alpha beta gamma OMEG delta =...
  44. Garlic

    I Question about the quantum harmonic oscillator

    Dear PF community, I am back with a question :) The solutions for the quantum harmonic oscillator can be found by solving the Schrödinger's equation with: Hψ = -hbar/2m d²/dx² ψ + ½mω²x² ψ = Eψ Solving the differential equation with ψ=C exp(-αx²/2) gives: -hbar/2m (-α + α²x²)ψ + ½mω²x²ψ = Eψ...
  45. Baibhab Bose

    Effects of KE & PE of a Harmonic Oscillator under Re-scaling of coordinates

    The wavefunction is Ψ(x,t) ----> Ψ(λx,t) What are the effects on <T> (av Kinetic energy) and V (potential energy) in terms of λ? From ## \frac {h^2}{2m} \frac {\partial^2\psi(x,t)}{\partial x^2} + V(x,t)\psi(x,t)=E\psi(x,t) ## if we replace x by ## \lambda x ## then it becomes ## \frac...
  46. PhillipLammsoose

    I Problem with the harmonic oscillator equation for small oscillations

    Hey, I solved a problem about a double pendulum and got 2 euler-lagrange equations: 1) x''+y''+g/r*x=0 2) x''+y'' +g/r*y=0 (where x is actually a tetha and y=phi) the '' stand for the 2nd derivation after t, so you can see the basic harmonic oscillator equation with a term x'' or y'' that...
  47. J

    Oscillator Frequency of a Ring Oscillator with RC feedback

    I'm not sure how will this oscillator work. Assume A is low, so B will be high and the capacitor will charge through B-C- 2Mohm. Now even D has gone high, so A will be high and B will be low and C will discharge. I'm not sure how the voltage divider rule across RC will take into effect. I found...
  48. Glenn Rowe

    A Feynman propagator for a simple harmonic oscillator

    I'm reading through Lancaster & Blundell's Quantum Field Theory for the Gifted Amateur and have got to Chapter 17 on calculating propagataors. In their equation 17.23 they derive the expression for the free Feynman propagator for a scalar field to be...
  49. D

    How should i start learning how to build an electronic oscillator?

    How should I start learning how to Build an electronic oscillator? Any voltage will do. It drives a led. Target frequency I 1000 hertz.
  50. D

    Crystal oscillator not working

    I bought a raltron crystal oscillator. I connected it to a programmable frequency divider. It is supposed to cause a diode to blink on and off. The crystal oscillator has a rated frequency of 100 megahertz. The programmable frequency divider can divide a frequency by up to 2,147,483,648. Diode...
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