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.

View More On Wikipedia.org
Recent contents Top users
  1. N

    Underdamped Harmonic oscillator with applied force

    Homework Statement An underdamped harmonic oscillator with mass m, spring constant k, and damping resistance c is subject to an applied force F0cosωt. (a) [analytical] If, at t = 0, x = x0 and v = v0, what is x(t)? Homework Equations Ωinitial = √(k/m) The Attempt at a...
  2. S

    Quantum Mechanics 3D harmonic oscillator

    What is the normalized ground-state energy eigenfunction for the three-dimensional harmonic oscillator V(r) = 1/2 m* ω^2 * r^2 Use separation of varaibles strategy. Express the wave function in spherical coordinates. What is the orbital angualar momentum of the ground state? Explain? I...
  3. J

    Critically Damped Oscillator Spring Constant and Damping Parameter

    Homework Statement A mass of 1000 kg drops from a height of 10.0 m onto a platform of negligible mass. It is desired to design a spring and damper on which to mount the platform so that it will settle to a new equilibrium position 2.00 m below its original position as quickly as possible...
  4. A

    Finding the maximum kinetic energy of a harmonic oscillator

    Homework Statement A harmonic oscillator with a vertical mass on a string has a hanging mass of 2m and a spring constant of K. It oscillates with an amplitude of Z. When its position is at a distance Z/2 of the equilibrium point, its potential energy is Ui. What is the maximum kinetic energy...
  5. B

    Forced Oscillator where Damping is Negligible

    Homework Statement Damping is negligible for a 0.139 kg mass hanging from a light 7.00 N/m spring. The system is driven by a force oscillating with an amplitude of 1.88 N. At what frequency will the force make the mass vibrate with an amplitude of 0.430 m? There are two possible solutions...
  6. S

    Instanton configurations of an even anharmonic oscillator

    Cheers everybody, the Hamiltonian of an even anharmonic oscillator is defined as H_N(g) = - \frac{1}{2} ∂_q^2 + \frac{1}{2} q^2 + g q^N (N even). In a paper (PRl 102, 011601) I found that to determine the eigenenergies of this system the Euclidean path integral formalism is used. They...
  7. C

    How can I improve the linearity of my VCO circuit design?

    I recently designed a circuit of VCO and obtained a plot for frequency v/s Vc(control voltage). The graph was pretty much linear for a certain range of Vc but tends to become non linear when Vc is further increased or decreased. How do I explain the non linearity...?? The schematic of...
  8. Y

    Underdamped Oscillator Solution: Deriving x(0) and v(0)

    Homework Statement Show that the underdamped oscillator solution can be expressed as x(t)=x_{0}e^{-γt}[cos(Ω't+((v_{o}+γx_{o})/(x_{o}Ω')sinΩ't] and demonstrate by direct calculation that x(0)=x_{o} and \dot{x}(0)=v_{o} Homework Equations The underdamped oscillator solution is...
  9. P

    Understanding Free Modes in Simple Harmonic Oscillators

    In the context of normal modes, what is a free mode? When the whole system is in motion?
  10. D

    What Do Entangled Eigenvectors Indicate in a Quantum Harmonic Oscillator?

    Hey, I'm doing a vacation scholarship at my university where I am helping a masters student with some of his research. We have a 3x3 lattice of coupled oscillators which we have determined the Hamiltonian of and applied the squeeze operator. We constructed a 18x18 conical Hamiltonian...
  11. L

    Curve fitting of a damped harmonic oscillator

    Homework Statement I was wondering if there was a general method for finding a function that fits a set of data for a damped harmonic oscillator I'm currently writing up a presentation on the experiment for the gravitational constant and the way i did the experiment was to use a torsion...
  12. J

    Classical Mechanics: Simple harmonic oscillator problem

    Homework Statement A simple harmonic oscillator with mass m = 1/2 and k = 2 is initially at the point x = √3 when it is projected towards the origin with speed 2. Find the equation of motion describing x(t). Homework Equations x=Asin(ωt+θ) The Attempt at a Solution At t=0...
  13. J

    Damped Oscillator and amplitude

    1. Homework Statement [/b] Consider the damped oscillator illustrated in the figure below. Assume that the mass is 365g, the spring constant is 112N/m, and b = 0.117kg/s. How long does it take for the amplitude to drop to half its initial value? (A*e-b*t/(2m))...
  14. P

    Solve Coupled Oscillator Problem from Goldstein's Classical Mechanics

    Hey, I've been trying to solve this question from Goldstein's Classical Mechanics. The picture I have of the question is from a later edition and the hint was removed from the question, the hint was let η3=ζ3...
  15. B

    Wien Bridge Oscillator: The Amazing Design Behind Car Technology

    Today I came across this design(as I am studying for my exams :P) And looking through my good Malvino, I found it. And I my mind was simply blown out by the concept of this oscillator. (If I got it right) http://pokit.org/get/957089cb8862c381d597a745b02c2763.jpg Malvino went here and there...
  16. G

    Harmonic oscillator with slight non-linearity

    I have an interesting problem I have come across in my research. It results in the differential equation as follows: x''+2γ(x')^\nu+\omega_{o}^2x=g(t) Primes indicate the derivative with respect to t. \gamma and \omega are constants. The non-linearity comes from the first derivative x'...
  17. T

    Harmonic Oscillator Potential Approximation

    Homework Statement A particle is in a region with the potential V(x) = κ(x2-l2)2 What is the approximate ground state energy approximation for small oscillations about the location of the potential's stable equilibrium? Homework Equations ground state harmonic oscillator ~ AeC*x2...
  18. C

    Time-Dependent Frequency Harmonic Oscillator

    Homework Statement Consider an harmonic oscillator with time-dependent frequency as: \omega (t)=\omega_0 * \exp^{- \lambda t} Find the time dependence of the ground state energy of this oscillator for \lambda << 1 situation. Homework Equations H=H_{0} + V(t) H_{0} = \frac{p^2}{2m} +...
  19. S

    Investigating Frequency Change in a Ring Oscillator

    Hello, I am hoping someone can give me some advice. I am playing about with the design of a ring oscillator in an electronics simulations package. The ring has 5 inverters. As part of the assignment we were asked to ad in an extra inverter to the output of the ring and see if there was a...
  20. U

    Damped oscillator consecutive amplitude ratio

    Homework Statement Undamped oscillator's period T_0 = 12s. Damped oscillator's angular frequency \omega_1 = \omega_0 * 97\% where \omega_0 is the angular frequency of the undamped oscillator's. What is the ratio of consecutive maximum amplitudes? Homework Equations Equation of damped...
  21. J

    Oscillator Problem Maximum speed & amplitude

    Homework Statement A 800g oscillator has a speed of 120.0 cm/s when its displacement is 1.5 cm and 55.0 cm/s when its displacement is 8.0 cm. a. What is the oscillator’s maximum speed? b. What is the oscillator’s maximum amplitude? Homework Equations A= sqroot(X^2+(V^2/w^2)...
  22. D

    Fortran Fortran Simple Harmonic Oscillator Problem

    Hello fellow computer physics nerds, I'm trying to write a program to plot the positions of the three particles connected by two springs (one dimensional) in Fortran 90. I have a main program block and a module that calls a PGPLOT. My problem is that the positions of the second and third...
  23. X

    Coupled Harmonic oscillator Setup

    I REALLY need help with this one guys! As of right now I believe I only need help with just the set up of the problem. The rest is just solving a differential equation and I assume the frequencies they want will just pop out. Homework Statement Two identical springs and two identical...
  24. G

    Particle in harmonic oscillator potential

    Homework Statement A particle with mass m moves in 3-dimensions in the potential V(x,y,z)=\frac{1}{2}m\omega^{2}x^{2}. What are the allowed energy eigenvalues?Homework Equations The Attempt at a Solution The Hamiltonian is given by H=\frac{P^{2}}{2m}+\frac{1}{2}m\omega^{2}X^{2} where P is the...
  25. D

    Rotational properties of the harmonic oscillator

    Hi everybody, This is my first post in this forum although I started following it some time ago. My question is related to rotational properties involving harmonic oscillator model. Homework Statement We are told to evaluate the expectation value of the rotational constant of a...
  26. C

    Quantum Harmonic Oscillator Differential Equation help

    Hi, so i am looking at the quantization of the harmonic oscillator and i have the following equation... ψ''+ (2ε-y^{2})ψ=0 I am letting y\rightarrow \infty to get... ψ''- y^{2}ψ=0 It says the solution to this equation in the same limit is... ψ= Ay^{m}e^{\pm y^{2}/2} The positive...
  27. S

    Bifurcations in a harmonic oscillator equation

    Hello everyone, I've been trying to figure out how to determine bifurcation values in a harmonic oscillator when either the spring constant α or damping coefficient β act as undefined parameters. I understand bifurcations in first-order DEs, but I can't figure them out in a second-order...
  28. A

    High Frequency Oscillator Circuit Help?

    Hey guys, I'm designing a wireless charging system, and I've managed to take some measurements between two coils for the voltage transfer, but the signal generator I'm using doesn't seem to output any measurable current. What could I do to it, or what could I design from scratch that...
  29. S

    Period doubling for a damped, driven, harmonic oscillator

    I'm not sure I'm in the right forum but I'll try and ask anyways. So I simulated a damped, driven pendulum in Java with the goal of showing period doubling/chaotic behavior. But then, as I was increasing the driving force, i saw the double period born. Then the 4-period...but then suddenly...
  30. N

    A Damped Oscillator and Negative Damping Force

    A damped oscillator is described by the equation m(x'') + b(x') + kx = 0, where the damping force is given by F = -b(x'). Show that the rate of change of the total energy of the oscillator is equal to the (negative) rate at which the damping force dissipates energy.
  31. N

    How does LC phase shift oscillator work?

    Heya Everyone :blushing: Im slightly confused as to how LC phase shift oscillator work ? Its a circuit consisting of 1 op-amp ( used as oscillator), 1 LC loop, few resistors. The op-amp has a reference voltage applied to the non-inverting end (+ve). The inverting end has a feedback...
  32. J

    Finding total energy of an oscillator

    Homework Statement Find the total energy of the following (mass m= 2 kg) oscillator. Homework Equations x=2cos(6∏t) The Attempt at a Solution Wouldn't I take my Amplitude of 2 and my period of 6 mulitply them together to get my max velocity of 12 then using KE = 1/2msquared I...
  33. fluidistic

    Quantum mechanics, harmonic oscillator and wavefunction

    Homework Statement A harmonic oscillator is initially in the state \psi (x,0)=Ae^{-\frac{\alpha ^2 x^2}{2}} \alpha x (2\alpha x +i). Where \alpha ^2 =\frac{m \omega}{\hbar}. 1)Find the wavefunction for all t>0. 2)Calculate the probability to measure the values \frac{5\hbar \omega }{2} and...
  34. tom.stoer

    SU(N) symmetry in harmonic oscillator

    Starting with the D-dim. harmonic oscillator and generators of SU(D) T^a;\quad [T^a,T^b] = if^{abc}T^c one can construct conserved charges Q^a = a^\dagger_i\,(T^a)_{ik}\,a_k;\quad [Q^a,Q^b] = if^{abc}Q^c satisfying the same algebra and commuting with the Hamiltonian H =...
  35. L

    Why are load capacitors necessary for crystal oscillators?

    Why does a crystal oscillator need load capacitors? Is it because there will be some capacitive load across the xtal pins?
  36. K

    Energies of a Quantum Harmonic Oscillator

    Hey guys I was just looking over a past homework problem and found something I'm not too sure on - A particle is in the ground state of a Harmonic potential V (x) = 0.5mω2x2 If you measured the energy, what are the possible results, and with what probabilities? Now I know the answer...
  37. A

    Exploring the Quantum Harmonic Oscillator: Eigenstates and Energies

    Homework Statement Consider the Hamiltonian H=\frac{p^2}{2M}+\frac{1}{2}\omega^2r^2-\omega_z L_z Determine its eigenstates and energies. 2. The attempt at a solution I want to check my comprehension; by eigenstate they mean \psi(r) from the good old H\psi(r)=E\psi(r) and...
  38. K

    How Do You Calculate the Vibrational Frequency of HCl from Spectroscopic Data?

    Homework Statement "Vibrational spectroscopic studies of HCl show that the radiation absorbed in a transition has frequency 8.63*10^13 Hz. Calculate the vibrational frequency of the molecule in this transition." Homework Equations E_n=(n+1/2)hv v=(1/(2pi))(sqrt(k/μ)) The Attempt...
  39. L

    Differential equation, coupled oscillator, relative movement

    Hi everyone Homework Statement Take a look at the drawing. Now I found out the differential equation for this is: \mu \vec{r}''=-k \vec{r} mu is the reduced mass Now I shall show, with using the generel solution for this differential equation (in cartesian coordinates), that the...
  40. S

    Energy of a simple harmonic oscillator

    Homework Statement To test the resiliency of its bumper during low-speed collisions, a 1000 kg automobile is driven into a brick wall. The car's bumper behaves like a spring with a force constant 5.00 x 106 N/m and compresses 3.16cm as the car is brought to rest. What was the speed of the car...
  41. G

    Find the expectation value of momentum squared for a simple harmonic oscillator

    Find the expectation value of (px)2, keeping in mind that ψ0(x) = A0e−ax2 where A0 = (2mω0/h)^1/4, and <x2> = ∫x2|ψ|2dx = h_bar / 2mω0 <ψ(x)|px2|ψ(x)> = ∫ψ(x)(pop2)ψ(x) dx pop = [hbar / i] (\delta/\deltax) I'm not going to attempt to type out me solving the integral because it...
  42. T

    Question Regarding Harmonic Oscillator Eigenkets

    Hi everyone! Given that a harmonic oscillator has eigenkstates |n> where n = 1,2,3,..., how can we calculate <X>, <P>, <X^2>, etc. Is there a need to define a wavefunction in the |n> basis? Thanks!
  43. C

    What is the velocity of an oscillator at a specific position?

    Homework Statement A simple harmonic oscillator has spring constant k = 7.8 N/m, amplitude A = 12 cm, and maximum speed 4.3 m/s. What's the oscillator's speed when it's at x = 5.4 cm? Homework Equations KE_max=1/2*k*A^2 KE=1/2mv^2 ma=-kx v=k/ma The Attempt at a Solution I...
  44. fluidistic

    Quantum mechanics, harmonic oscillator

    Homework Statement Consider a classical particle in an unidimensional harmonic potential. Let A be the amplitude of the oscillation of the particle at a given energy. Show that the probability to find the particule between x and x+dx is given by P(x)dx=\frac{dx}{\pi \sqrt {A^2-x^2}}. 1)Graph...
  45. F

    Oscillator with and without damping - Need help please

    An oscillator with natural frequency ω consists of a mass on a spring positioned on a horizontal table. The table is frictionless for x<0 but has friction for x>0 and an effective damping constant K on that side of the table. Find the frequency of this oscillator and the ratio of successive...
  46. F

    Help with oscillator problem before class please/thank you.

    I can't seem to figure out how to derive this relation, so a first step or any suggestions would be greatly appreciated. Thank you in advance. Homework Statement After four cycles the amplitude of a damped harmonic oscillator has dropped to 1/e of its initial value. Find the ratio of the...
  47. G

    Energy of an damped/undriven oscillator in terms of time?

    Homework Statement The Q asks to show that the time rate of change in mechanical energy for a damped, undriven oscillator is dE/dt=-bV^2.Homework Equations I assume you take the derivative of the total E eq, E=(1/2)mV^2 + (1/2)kx^2 but I'm unsure how to put the E eq into terms of t, like...
  48. L

    Understanding Double Oscillator Potential Eigenstates and Tunneling

    Homework Statement 1. Consider the problem of a particle of mass m moving in the double oscillator potential V(x) = ½ k ( |x| - a )2 which has two wells centered at x = ±a separated by a barrier whose height at the origin is given by V0 = ½ k a2 . The particle can tunnel from one...
  49. F

    Sudden barrier removal to half harmonic oscillator

    Homework Statement A particle is in the ground state of a half harmonic oscillator (V=m/2 w^2 x^2 x>0, and infinity x<0). At t=0, the barrier at x=0 is suddenly removed. Find the possible energy measurements as a function of time and the wavefunction for all times. Homework Equations <H>...
  50. F

    How Does Initial Displacement Affect Different Damped Harmonic Oscillators?

    Homework Statement A damped harmonic oscillator is displaced a distance xo from equilibrium and released with zero initial velocity. Find the motion in the underdamped, critically damped, and overdamped case. Homework Equations d2x/dt2 + 2K dx/dt + ω2x = 0 Underdamped: x =...
Back
Top