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

    Energy of electron-hole pairs in 3D space

    Dear All: I'm trying to use fluctuation dissipation theorem to describe spontaneous photon emission process by electron-hole recombination in semiconductor material. I notice that all the references using such a method considers the dipole's degree of freedom separately, for example in x, y, z...
  2. D

    Quantum oscillator from position to momentum space

    So I've read you can get the corresponding wave function of a quantum harmonic oscillator in momentum space from position space by making the substitution ##x \to k## and ##m \omega \to 1/m \omega##. However in deriving the TISE for momentum space, I seem to be making a mistake. In momentum...
  3. D

    Quantum harmonic oscillator inner product

    Homework Statement Using the equations that are defined in the 'relevant equations' box, show that $$\langle n' | X | n \rangle = \left ( \frac{\hbar}{2m \omega} \right )^{1/2} [ \delta_{n', n+1} (n+1)^{1/2} + \delta_{n',n-1}n^{1/2}]$$ Homework Equations $$\psi_n(x) = \left ( \frac{m...
  4. baby_1

    Design oscillator with linear small S parameters

    Hello I have a question about design oscillator with linear small S parameters.If you assume I use a Common emitter configuration and put my resonator at input port (Base/Emitter). After I select a Gama(G) in unstable region in input smith chart plane(for example Gama(G)=A<B (for example A=1))...
  5. S

    Simple Harmonic Oscillator Zero Probability Points

    Hi, What is the physical meaning of zero probability of finding a particle in the square of the Quantum SHO wave function? the particle is supposed to oscillate about the equilibrium position, how would it go from an end point to the other end point without passing by certain points? Could the...
  6. AwesomeTrains

    Maximum position expectation value for 1D harmonic oscillator

    Hey, I'm stuck halfway through the solution it seems. I could use some tips on how to continue. 1. Homework Statement I have to determine a linear combination of the states |0\rangle, |1\rangle, of a one dimensional harmonic oscillator, so that the expectation value \langle x \rangle is a...
  7. P

    What is the Normalized Ground State Energy of a 3-D Harmonic Oscillator?

    Homework Statement What is the normalized ground state energy for the 3-D Harmonic Oscillator Homework Equations V(r) = 1/2m(w^2)(r^2) The Attempt at a Solution I started with the wave fn in spherical coordinates, and have tried using sep of variables, but keep getting stuck when trying to...
  8. ChrisVer

    C++ Harmonic Oscillator (with Force)

    I was wondering whether it's possible to write a code in C++ that would be able to solve the Harmonic Oscillator: \ddot{x} + \gamma x = F_{external}(t,x) With different F function inputs... I thought about creating a function with if clauses, so for different inputs by the user, the force F...
  9. R

    Hamiltonian of the Half Harmonic Oscillator

    Given the half harmonic potential: \begin{equation}V=\begin{cases}1/2\omega^2mx^2 & x > 0\\\infty & x < 0\end{cases}\end{equation}What will be the Hamiltonian of the half oscillator?I understand that for x>0 the Hamiltonian will be...
  10. shanepitts

    Average kinetic energy of harmonic oscillator

    I was wondering why the average kinetic energy is calculated in this manner. They are dividing the kinetic energy function by the period (noted here as To) and integrating it with limits from 0→To. Why? (This is a tiny portion of a larger textbook example, not an actual assignment.) Sorry for...
  11. T

    555 timer IC - Calculating resistance needed

    Voltage = 9.0 V, Current = 20 mA, Capacitor (C) = 10 microF, Resistance before (too high) [R_A = R_B] = 10 k Ohms. In a a-stable oscillator, calculating the resistance needed for two resistors (R_A = R_B) to discharge and charge a capacitor (C) so that a LED does not blow. Currently my circuit...
  12. C

    Normalisation of harmonic oscillator classical action

    Homework Statement The transition amplitude for the harmonic oscillator may be written as ##\langle x_2, t_2 | x_1, t_1 \rangle = N_{\omega}(T) \exp(i/\hbar S_{cl})##, where ##T=t_2-t_1## and ##S_{cl}## is the classical action. Let the wave function at ##t=0## be ##\psi(x,o) =...
  13. R

    Quantum Mechanics: Harmonic Oscillator

    Homework Statement A particle of mass m in the one-dimensional harmonic oscillator is in a state for which a measurement of the energy yields the values ##\hbar\omega/2## or ##3\hbar\omega/2## each with a probability of one-hald. The average value of the momentum ##\langle p_x\rangle## at...
  14. helofrind

    Building a 555 Astable Oscillator: Achieving 50KHz Output

    So I built a 555 astable oscillator. I wanted to get 50 KHz on my output, which I have achieved, but the values of my components do not match the formula I have calculated. I have: R1 = 98 ohms R2 = 67 ohms Cap = 100nF So I have: 1.44/(98 + 2 67) 100nF Which should be 62KHz. Also can anyone...
  15. T

    Engineering Analyzing an Oscillator Circuit: Voltage and Current Dynamics

    I have the following circuit that I need to calculate the voltage across the capacitor as a function of time. Standard variables for the component values, voltage drops, currents, ect. You'll notice that the voltage (at the top right corner) oscillates at a frequency dependent on the...
  16. D

    Harmonic oscillator in Heisenberg picture

    For the harmonic oscillator in 1-D we get the 2nd time derivative of the x Heisenberg operator = -ω2 x. When that is integrated it gives xH (t) = Acos(ω t) +Bsin (ω t) where A and B are time independent operators. My question is why are the constants A and B incorporated into the terms as a...
  17. S

    Derive equation for Energy of the Harmonic Oscillator

    I'm trying to figure out how to derive the equations for Energy from the differential equation corresponding to the (simple and damped) harmonic oscillator. Please note that I don't want to start with the expressions for kinetic and potential energy, I want to derive them. The references that I...
  18. Runei

    Harmonic oscillator shifted origin

    Hello, I'm was going through the simple harmonic oscillator, just as a recap, and I stumbled upon something which is causing me wonder. I'm solving the SHO with a shifted origin, and so I have the differential equation F=-k(x-x_0) \ddot{x}=-\frac{k}{m}x+\frac{kx_0}{m} Now, I get that I can...
  19. Entanglement717

    1D Harmonic Oscillator in a Constant Electric Field

    Homework Statement Hello, I'm just curious as to whether I'm going about solving the following problem correctly... Problem Statement: A particle mass m and charge q is in the ground state of a one -dimensional harmonic oscillator, the oscillator frequency is ω_o. An electric field ε_o is...
  20. A

    How do you plot eigenfunctions of perturbed HO?

    Homework Statement Find eigenvalues and eigenvectors of a perturbed harmonic oscillator (H=H0+lambda*q4 numerically using different numerical methods and plot perturbed eigenfunctions. I wrote a code in c++ which returns a row of eigenvalues of the perturbed matrix H and a matrix of...
  21. C

    Relationship between size and frequency of an oscillator

    I've always just accepted that as you scale down a mechanical system the frequency and Q factor both increase. For example, this Wikipedia page simply says that "Small bells ring at higher frequencies than large bells". But for a driven damped harmonic oscillator, what is the exact relationship...
  22. P

    Undamped Harmonic Oscillator Problem

    Homework Statement Find the initial conditions for 2 interchangeable harmonic oscillators (undamped) so that they have the same amplitude of oscillation. Homework Equations x(t)=Xm*cos(wt+ϕ)The Attempt at a Solution The amplitude of the function is given by Xm so I would have thought that just...
  23. Futurestar33

    Given a harmonic oscillator with mass m, and spring constant

    Homework Statement Given a harmonic oscillator with mass m, and spring constant k, is subject to damping force F= cdx/dt and driven by an external force of the form F[ext]= FoSin(wt). A) Find the steady state solution. B) Find the amplitude and the phase. Homework Equations F=-kx the steady...
  24. P

    Classical Limit of a Quantum Harmonic Oscillator

    I seem to have two approaches that I've seen and understand, but I can't quite see how they relate. 1. Write a general time evolving state as a superposition of stationary states multiplied by their exp(-iEt/h) factors, and calculate <x>. We find that <x>=Acos(wt+b) as in classical physics (in...
  25. N

    Designing a PSPICE Ring Oscillator with CMOS Inverters | Homework Help

    Homework Statement I'm required to design a simple ring oscillator... One with three stages of cascaded cmos inverters using pspice capture(student version) Homework EquationsThe Attempt at a Solution I have simulated the circuit with a 5v supply but all i see is a dc line at 2.50v.has this...
  26. A

    Designing a variable-frequency ultrasonic wave generator

    Hello everyone! Seeing as this is my first post, I'll give you a basic background of who I am: My name is Andrew Raisbeck; I graduated from university with a Bachelor of Computing (Computer Science) degree a little over a year ago, and I now work full-time for the government of Canada. Since I...
  27. gfd43tg

    Ladder operators to find Hamiltonian of harmonic oscillator

    Hello, I was just watching a youtube video deriving the equation for the Hamiltonian for the harmonic oscillator, and I am also following Griffiths explanation. I just got stuck at a part here, and was wondering if I could get some help understanding the next step (both the video and book...
  28. D

    Harmonic oscillator in 2D - applying operators

    Hello, I juste don't know how this was done it is on the solutionnary of a very long exercise and i am not getting this calculation 1. Homework Statement <1,0| ax+ay++ax+ay+axay++axay|0,1> = <1,0|1,0> Homework Equations 3. The Attempt at a Solution We have that |0,1> = ay+ |0,0> I don't...
  29. J

    Help with relaxation oscillator

    All, I am confused as to exactly how the capacitive relaxation oscillator works. From the diagram above: Because the lamp is in parallel, why is it not immediately receiving the voltage necessary to light instantly? Thanks.
  30. C

    Degenerate perturbation theory for harmonic oscillator

    Homework Statement [/B] The isotropic harmonic oscillator in 2 dimensions is described by the Hamiltonian $$\hat H_0 = \sum_i \left\{\frac{\hat{p_i}^2}{ 2m} + \frac{1}{2} m\omega^2 \hat{q_i}^2 \right\} ,$$ for ##i = 1, 2 ## and has energy eigenvalues ##E_n = (n + 1)\hbar \omega \equiv (n_1 +...
  31. H

    Can the Lorentz Oscillator Model be Modified to Include Radiation Force?

    Hi Guys, I'm looking into the Lorentz model Since the acceleration/de-acceleration of electron can cause radiation hence create force, can anyone tell me how to modify the above equation to include the term of radiation force? Thanks. jack
  32. Q

    Wave Generator with Crystal Quartz Oscillator?

    Hi All! A little background info. I'm working with cardiac pacemaking devices with the overall scope of implementing piezoelectric energy harvesters into the devices. I'm in the initial stages of research and development. Okay, so this is my conundrum: I have an output pulse circuit as shown...
  33. E

    Quantum harmonic oscillator: average number of energy levels

    Homework Statement I must find the average number of energy levels of quantum harmonic oscillator at temperature T, and the answer is given as I must use Boltzmann distribution and the sum of geometric progression. For finding the average value I must use the equation <F>=trace(F*rho)...
  34. T

    Driven harmonic oscillator problem

    Homework Statement A mass m sits on a horizontal frictionless surface and is attached to a wall by means of a spring having force constant k. The mass is now subjected to an additional force of the form. F(t) = Acosbt (a) Write the equation of motion for this mass.(b) What is the solution to...
  35. D

    Understanding a Colpitts oscillator

    As I was playing around with a small AM oscillator, I thought it would be time to understand how they actually work. I am referring to the 3rd picture on this page (base mode): http://elektroniktutor.oszkim.de/signalkunde/colpitts.html Given the working point of the transistor, I describe its...
  36. S

    Derivation of van der pol oscillator

    Homework Statement Given characteristic equation for a circuit containing a diode, I must figure out how to fit a polynomial to the curve so that the van der pol equation is obtained. The paper I am reading is here: http://www.unige.ch/math/hairer60/pres/pres_rentrop.pdf My doubts are...
  37. Coffee_

    QM, the convergence of the harmonic oscillator function.

    1. After finding out that the wave function ##\Psi(z) \sim Ae^{\frac{-z^{2}}{2}}## in the limit of plus or minus infinity Griffiths separates the function into two parts ##\Psi(z)=h(z)e^{\frac{-z^{2}}{2}}## My question will be about a certain aspect of the function ##h(z)## After solving the...
  38. Domenico94

    Solar panels and optical parametric oscillator

    Hi everyone. On these days, by watching solar panels and similar stuff, I just thought about it, and why they take such a wide surface to produce energy, and why their output is often low, as we all know. By navigating here on the internet, I've just seen a device called OPO (Optical...
  39. darkbasic

    Colpitts oscillator PSPICE

    Hi, I'm trying to simulate exercise 13.21(a) from Sedra-Smith, with: Vcc=5V f=100 kHz and the following BJT model: .model modn NPN(Is=6.734f Xti=3 Eg=1.11 Vaf=74.03 Bf=416.4 Ne=1.259 Ise=6.734f Ikf=66.78m Xtb=1.5 Br=.7371 Nc=2 Isc=0 Ikr=0 Rc=1 Cjc=3.638p Mjc=.3085 Vjc=.75 Fc=.5 Cje=4.493p...
  40. A

    Quantum harmonic oscillator tunneling puzzle

    My problem is described in the animation that I posted on Youtube: For the sake of convenience I am copying here the text that follows the animation: I have made this animation in order to present my little puzzle with the quantum harmonic oscillator. Think about a classical oscillator, a...
  41. E

    First Year Forced Oscillator Problem

    Homework Statement Damping is negligible for a 0.164 kg mass hanging from a light 6.70 N/m spring. The system is driven by a force oscillating with an amplitude of 1.77 N. At what frequency will the force make the mass vibrate with an amplitude of 0.500 m? There are two possible solutions...
  42. V

    Damped Driven Harmonic Oscillator.

    Homework Statement An oscillator with mass 0.5 kg, stiffness 100 N/m, and mechanical resistance 1.4 kg/s is driven by a sinusoidal force of amplitude 2 N. Plot the speed amplitude and the phase angle between the displacement and speed as a function of the driving frequency and find the...
  43. R

    Calculating energy left in oscillator after 3 cycles

    Homework Statement Calculate how much original energy the oscillator in will have left after three cycles. Using Q= (ω/Δω) I have calculated the Q factor to be 4 Homework Equations The answer can be obtained by using the equation Q=2π(E/ΔE) Where ΔE/E is the fractional energy loss per...
  44. A

    Crystal Oscillator Package (4 pins)

    Homework Statement I'm trying to hook up crystal oscillator package on breadboard and test for expected operation: I'm not sure how and cannot find any data sheets for the pin connection diagrams, I attached an image I found of the kind of package I'm using. There are four pins. Homework...
  45. D

    Coherent States of Harmonic Oscillator

    Homework Statement Given the coherent state of the harmonic oscillator |z>=e^{-\frac{|z|^2}{2}}\sum_{n=0}^\infty\frac{z^{n}}{\sqrt{n!}}|n> compute the probability for finding n quanta in the sate |z> and the average excitation number <z|n|z>Homework Equations...
  46. S

    How Is the Turn-Ratio n Estimated in a Common-Emitter Oscillator?

    Homework Statement estimate the value of turn-ratio n [/B] R1=4.7 kΩ, R2=24 kΩ, Rl=2.7 kΩ, hfe=250, hoe=10^-5, hie=4 kΩ Homework Equations loop gain=1/n[hfe/hie*R'l] R'l=Rl||hoe||[n^2(R1||R2)] [/B] The Attempt at a Solution loop gain=1 [/B]
  47. C

    Find Energy Levels for Harmonic Oscillator w/ Stretch-Only Spring

    for harmonic oscillator, V(x) = 1/2*m*w^2*x^2. here, the spring can be stretch or compress. however, is if the spring can only stretch such that V(x) is infinity for x<0, then find energy level for this setup. I don't understand the part about spring only being able to stretch. what does that...
  48. mbijei

    Quantum harmonic oscillator in electric field

    Homework Statement There is a harmonic oscillator with charge q and sudenly we turn on external electric field E, which direction is the same as oscillator's. We need to find probability, that particles energy calculated in electric field will be in m state. n=1, m=2 2. Homework Equations The...
  49. grandpa2390

    What is the energy loss of damped oscillator

    Homework Statement what is the energy loss of the damped oscillator. Homework Equations x(t) = A*e^(-Bt)*cos(w1*t) T = 1/2 mv^2 The Attempt at a Solution To solve for an undamped oscillator, I took the derivative of the equation of motion x(t) and plugged the amplitude into 1/2 mv^2 equation...
  50. J

    Green function for forced harmonic oscillator

    Homework Statement The problem requires to solve the integration to find ## G(t) ## after ##G(\omega)## is found via Fourier transform. We have G(\omega)= \frac{1}{2\pi}\frac{1}{\omega _{0}^2 - \omega ^2} Homework Equations As mentioned previously, the question asks to find ##G(t)## The...
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