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. H

    Question about a harmonic oscillator integral

    Hi, I'm trying to learn quantum physics (chemistry) on my own so that my work with Gaussian and Q-Chem for electronic structural modeling is less of a black box for me. I've reached the harmonic oscillator point in McQuarrie's Quantum Chemistry book and I'm having trouble justifying a step in...
  2. C

    Minimum and maximum uncertainty values in quantum harmonic oscillator

    Homework Statement I have to find the minimum and maximum values of the uncertainty of \Deltax and specify the times after t=0 when these uncertainties apply. Homework Equations The wave function is Ψ(x, 0) = (1/√2) (ψ1(x)+ iψ3(x)) and for all t is Ψ(x, t) = (1/√2)...
  3. C

    Ladder operators and harmonic oscillator

    1. Explain why any term (such as AA†A†A†)with unequal numbers of raising and lowering operators has zero expectation value in the ground state of a harmonic oscillator. Explain why any term (such as AA†A†A) with a lowering operator on the extreme right has zero expectation value in the...
  4. C

    Harmonic oscillator kinetic energy

    Homework Statement Calculate the expected value of the kinetic energy being \varphi(x,0)=\frac{1}{\sqrt{3}}\Phi_0+\frac{1}{\sqrt{3}}\Phi_2-\frac{1}{\sqrt{3}}\Phi_3 Homework Equations K=\frac{P^2}{2m} The Attempt at a Solution I tried to solve it using two diffrent methods and...
  5. C

    How Does the 3D Harmonic Oscillator Model Extend from 1D Solutions?

    Homework Statement Consider a particle of mass m moving in a 3D potential V(\vec{r}) = 1/2m\omega^2z^2,~0<x<a,~0<y<a. V(\vec{r}) = \inf, elsewhere. 2. The attempt at a solution Given that I know the solutions already for a 1D harmonic oscillator and 1D infinite potential well I'm going to...
  6. F

    Atom Stability and harmonic oscillator

    Why does in QM the electron does not fall toward the nucleus? After all, the only force between nucleus and electron is attractive. It seems that the electron can and does indeed fall toward the center in <simple harmonic oscillator>? My question is what's so different in these two systems...
  7. R

    Wevelength of sinusoidal wave generated by oscillator

    A sinusoidal wave is traveling along a rope. The oscillator that generates the wave completes 40.0 vibrations in 30.0 s. Also, a given maximum travels 425 cm along the rope in 10.0 s. What is the wavelength?
  8. C

    Harmonic Oscillator - Normalization

    Homework Statement Trying to normalize the first excited state. I have, 1 = |A_1|^2(i\omega\sqrt{2m}) \int_{-\inf}^{\inf} x \exp(-m\omega x^2/2\hbar) How do I do the integral so I don't get zero since it's an odd funciton?
  9. 3

    Normalizing psi in harmonic oscillator

    My question is pretty easy (i think). I have a wavefcn PSI defined at t=0. The PSI is a mix of several eigenstates. Let's say PHI(x,0)=C1phi1 + C2 phi3. Now C1 and C2 are given to me, so I am wondering is this wavefcn. already normalized, or do i have to normalize it despite definite C1 and C2...
  10. G

    Polyatomic quantum harmonic oscillator

    Hi! Would anyone be able to point me toward a detailed explanation of determining the Hamiltonian of a polyatomic quantum oscillator? My current text does not explain the change of coordinates ("using normal coordinates or normal modes") in detail. All I can find is material on a diatomic...
  11. N

    Anharmonic Oscillator Heat Capacity

    Homework Statement Consider the anharmonic potential U(x)=cx2-gx3-fx4 and show that the approximate heat capacity of the classical unharmonic oscillator in one dimension is C=kb[1+(3f/2c2+15g2/8c3)kbT] Homework Equations U(x)=cx2-gx3-fx4 and heat capacity is C=dU/dT The...
  12. N

    How to Calculate Heat Capacity of One-Dimensional Anharmonic Oscillator?

    Hi, I want to calculate heat capacity of anharmonic oscillator in one dimension. Does anyone have an idea? Thanks...
  13. T

    Quantum harmonic oscillator

    Can someone tell me if there is a difference in the moving motion between a quantum harmonic oscillator and a simple harmoic oscillator. Also, does anoyone know a good site where i could learn more on quantum harmonic oscillator. ty
  14. O

    Frequency of Harmonic Oscillator w/ Gravitational Force

    The frequency of a harmonic oscillator is (as you know) f=\frac{1}{2\pi}\sqrt{\frac{k}{m}} I am wondering if this equation only applies for massless harmonic oscillators (or oscillators oscillating sideways)? The proof for the equation above is \sum {F=ma} -kx=ma...
  15. L

    Relativistic quantum harmonic oscillator

    The question is as follows: Suppose that, in a particular oscillator, the angular frequency w is so large that its kinetic energy is comparable to mc2. Obtain the relativistic expression for the energy, En of the state of quantum number n. I don't know how to begin solving this question. I...
  16. S

    Proof of average energy of quantum oscillator

    proove that the average energy of a quantum oscillator = hw/(e^(hw/kT)-1) where h= h bar w=omega k=boltzmann constant T=temp
  17. C

    Degenerate states of 2 particles in a 1D harmonic oscillator potential

    Homework Statement "Two non-interacting particles are placed in a one-dimensional harmonic oscillator potential. What are the degeneracies of the two lowest energy states of the system if the particles are a)identical spinless bosons b)identical spin-1/2 fermions? Homework Equations...
  18. K

    3-dimensional harmonic oscillator (quantum mechanics)

    Homework Statement 3-dimensional harmonic oscillator has a potetnial energy of U(x,y,z)=\frac{1}{2}k'(x^2+y^2+z^2). a) Determine the energy levels of the oscillator as a function of angular velocity. b) Calculate the value for the ground state energy and the separation between adjacent...
  19. L

    How can I derive the period of oscillation for a relaxation oscillator?

    Homework Statement I am having a bit of trouble with a homework problem on relaxation oscillators, the schematic is shown below: https://webspace.utexas.edu/sz233/Relaxation%20Oscillator.png The original problem states: derive a relationship for the period of oscillation for a relaxation...
  20. maverick280857

    Harmonic Oscillator energy = WKB approximate energy why?

    Hi, Why is it that the WKB approximation produces the correct eigenvalues for the Harmonic Oscillator problem, but the wrong wavefunctions, whereas for the square well, we get correct wavefunctions and the wrong eigenvalues? I've been trying to dig through the approximations we make in...
  21. W

    Harmonics Oscillator Homework: Solving Schrodinger Equation

    Homework Statement Show: \psi_1=N x e^{-\frac{x^2}{\sigma}} is an eigenfunction of the total energy operator(H). Homework Equations psi=N x exp[-x^2/K]The Attempt at a Solution I plugged in the above to the Schrodinger Equation-time indep. for Harmonic oscillator but I keep getting an x^2...
  22. T

    Lagranguan / Coupled Oscillator

    Homework Statement WIthin the framework of an idealised model, let a square plate be a rigid object with side "w" and mass "M", whose corners are supported by massless springs, all with a spring constant "k". The string are confined so they stretch and compress vertically with upperturbed...
  23. T

    Lagranguan / Coupled Oscillator

    moved to Advanced Physics Section seemed more relevant link to it is https://www.physicsforums.com/showthread.php?p=2169513#post2169513" Sorry for the double post in two spots if this can be removed Thanks Heeps
  24. Spinnor

    U(1):?:SU(3) 1D:2D:3D harmonic oscillator.

    The one dimensional harmonic oscillator is associated with the group U(1) and the three dimensional harmonic oscillator is associated with the group SU(3). Is their a group associated with the two dimensional harmonic oscillator? Thank you for any thoughts.
  25. M

    What exactly is an oscillator in quantum physical context?

    I've recently purchased a book on Quantum Physics, and I'm trying to get the basics down. At this point in time, I'm reading up on how Planck proposed that oscillators can only oscillate at discrete energies as opposed to on any amount of energy (on a theoretical continuous spectrum). This came...
  26. F

    3-d harmonic oscillator and SU(3) - how to imagine it?

    The 3-dimensional harmonic oscillator has SU(3) symmetry. This is stated in many papers. It seems to be due to the spherical symmetry of the system. (After all, the idea of a 3d harmonic oscillator is that a mass is attached to the origin with a spring, and that the mass can move in 3...
  27. M

    How Does Simple Harmonic Motion Affect Velocity and Energy in a Spring System?

    A 2.6 kg block is attached to a horizontal spring and undergoes simple harmonic motion on a frictionless surface according to the graph shown above. (a) What is maximum velocity of the box? (b) What is the mechanical energy of the box? now the wave is -sin wave but crosses the x-axis...
  28. F

    What is the period of a damped oscillator with given parameters?

    Homework Statement Hi guys the question is: a mass spring-damper system is positioned between two rigid surfaces, if mass m = 200g, spring constant k = 80 Nm-1, and damping pot of coefficient 65 gs-1. The mass is pulled 5cm down from its equilibrium position and then released. What is the...
  29. F

    Exploring the Lowest Energy State of Simple Harmonic Oscillator

    Homework Statement The wave function \Psi(x,t) ofr the lowest energy state of simple harmonic oscillator, consisting of a particle mass m acted on by a linear restoring force F=Cx, where C is the force constant, can be expressed as.. \Psi(x,t)=Aexp[-(\sqrt{}Cm/2h)x^{}2-(i/2)(\sqrt{}C/m)t]...
  30. P

    Generalized coordinates of a couple harmonic oscillator

    Homework Statement Suppose there is a square plate, of side a and mass M, whose corners are supported by massless springs, with spring constants K, K, K, and k <= K (the faulty one). The springs are confined so that they stretch and compress vertically, with unperturbed length L. The...
  31. N

    QM: Harmonic oscillator expectation value of position for t>0

    Homework Statement Hi all. At time t<0 a particle is in the stationary state \left| {\psi _0 } \right\rangle of the harmonic oscillator with frequency omega1 (i.e. the ground state of the H.O.). At t=0 the Hamiltonian changes in such a way that the new angular frequency is omega =...
  32. S

    How Do You Design and Troubleshoot a Ring Oscillator in PSpice?

    Design a digital ring oscillator using logic inverters that have propagation delay times of tPLH = 28ns and tPHL = 42ns. The Attempt at a Solution I'm using a general ring oscillator design using 3 CMOS inverters like this...
  33. I

    Normal modes of oscillator

    Homework Statement I'm reading Landau's Mechanics, in section 23, he discusses the oscillations with more than one degree of freedom, the Lagrangian is L = \frac{1}{2}\left(m_{ik}\dot{x}_i\dot{x}_k - k_{ik}x_ix_k\right) where m_{ik},k_{ik} are symmetric constants, and the summation over...
  34. A

    How Do You Solve a Damped Harmonic Oscillator Driven by a Sinusoidal Force?

    Homework Statement A damped harmonic oscillator is driven by a force F external= F sin (omega * t) where F is a constant, and t is time. Show that the steady state solution is given by x(t)= A sin (omega * t - phi) where A is really A of (omega), the expression for the amplitude...
  35. T

    Simple harmonic oscillator- the probability density function

    How to find the probability density function of a simple harmonic oscillator? I know that for one normal node is should be a parabola but what is the formula and how do we derive it?
  36. N

    Finding amplitude of oscillator

    Homework Statement a 200g mass attached to a horizontal spring oscillates at a frequency of 2.0 Hz. At t=0s, the mass is at x=5.0 cm and has v=-30 cm/s. Determine: a) period b)angular frequency c) AMPLITUDE Homework Equations x(t)=Acos(wt+psi) v(t)=-Awsin(wt+psi) w=2*pi*f T=1/f...
  37. A

    Damping in Duffing driven-anharmonic oscillator

    Greeting every one. In Duffing equation, the damping coeffecient usually assume possitive values (<<1). However, at certain cases, the damping coeffecient may asume negative values. Can anyone explain the meaning of positive and negative damping in Duffing equation as well as in real physical...
  38. R

    Solve Coupled Oscillator Homework: Find 2 Eigenfrequencies

    Homework Statement A thin hoop of radius R and mass M oscillates in its own plane with one point of the hoop fixed. Attached to the hoop is a small mass M constrained to move (in a frictionless manner) along the hoop. Consider only small oscillations, and show that the eigenfrequencies are blah...
  39. K

    QM: expectation value of a harmonic oscillator (cont.)

    Thanks for all the help on the first question but now I have to solve for <T>. I have no idea how to do this, and I could use some help for a kick start. thanks!
  40. K

    QM: expectation value of a harmonic oscillator

    first post! but for bad reasons lol Im trying to find <x> and <p> for the nth stationary state of the harmonic potential: V(x)=(1/2)mw^2x^2 i solved for x: x=sqrt(h/2mw)((a+)+(a-)) so <x> integral of si x ((a+)+(a-)) x si. therefor the integral of si(n+1) x si + si(n-1) x si. si(n+1)...
  41. M

    Engineering Why is the LC Oscillator Circuit Called a TANK Circuit?

    Why the LC oscillator ckt. is also known as a TANK ckt.?
  42. G

    Harmonic oscillator in a time-dependent force

    In quantum mechanics, one of the major concerns is the propagator determination of the system. The propagator is completely expressed in terms of its classical in the Van-Vleck Pauli Formula. In a harmonic oscillator in a time dependent force, the Lagrangian is given by...
  43. M

    Energy of driven damped oscillator

    Hi all! I was considering the Energy of a driven damped oscillator and came upon the following equation: given the equation of motion: m\ddot x+Dx=-b\dot x+F(t) take the equation multiplied by \dot x m\ddot x\dot x+Dx\dot x=-b\dot x^2+F(t)\dot x and we rewrite it...
  44. D

    Engineering Discover the Versatility of Opamp Oscillator Circuits for Audio Devices

    One application of an opamp can clearly be seen from a set of speakers for instance, but what about an oscillator circuit? What would be a good, clear, example of an application of an oscillator?
  45. D

    HCl Bohr Quantum Oscillator

    Homework Statement What
 is 
the 
wavelength 
of 
the 
emitted
 photon 
when
 HCl
 de‐excites 
from
 the
 first vibrational 
state? Well, I had to solve for the energy of the first vibrational state in the question before, assuming that it behaved like a harmonic oscillator using the...
  46. A

    Hermite Polynomials As Part of the Solution to the Harmonic Oscillator

    Homework Statement When trying to generate solutions to the harmonic oscillator, I'm trying to use hermite polynomials. I understand that there's a recursive relationship between the hermite polynomials but I'm confused in how each hermite polynomial is generated. Homework Equations...
  47. R

    How Do You Solve a Damped Harmonic Oscillator Differential Equation?

    damped harmonic oscillator, urgent help needed! Homework Statement for distinct roots (k1, k2) of the equation k^2 + 2Bk + w^2 show that x(t) = Ae^(k1t) + Be^(k2t) is a solution of the following differential equation: (d^2)x/dt^2 + 2B(dx/dt) + (w^2)x = 0 Homework Equations The...
  48. C

    Linear Simple Harmonic Oscillator: period a direct linear proportion to mass?

    If a mass that hangs suspended vertically from a spring is increased, then won't the period increase as a direct linear proportion? (Because the larger mass has a greater inertia and will require a larger force and longer time to change the direction of motion on each oscillation?) Some...
  49. A

    Finding the mean-square position for quantum harmonic oscillator

    Homework Statement Hi, Could someone give me a tip or two for how to calculate the mean square position ( <x^2>) for a linear quantum harmonic oscillator? Homework Equations I think I'm supposed to use the following recursion relation for Hermite polynomials: yHv=vHv-1 + .5Hv+1 the...
  50. P

    Driven Harmonic Oscillator - Mathematical Manipulation of Equations

    1. Homework Statement and the attempt at a solution Please see attached. I'm not so sure if my problem lies with the physics or the mathematics. I have the distinct feeling that it's the latter and that I'm missing something elementary, but truly have no idea how to proceed. Any...
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