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. O

    Forced Oscillator with unfamiliar forcing function and constants

    Homework Statement A force Fext(t)=F0[1-e(-a*t)] acts, for time t>0, on an oscillator which is at rest at x=0 at time 0. The mass is m; the spring constant is k; and the damping force id -b dx/dt. The parameters satisfy these relations: b=mq and k=4mq2 where q is a constant with units...
  2. O

    Damped oscillator given odd initial conditions

    Homework Statement (A) The damped oscillator is described by the equation mx''+bx'+kx=0. What is the condition for critical damping expressed in terms of m,b,k. Assume this is satisfied. (B) For t<0 the mass is at rest (x=0). This mass is set in motion at t=0 by a sharp impulsive force so...
  3. O

    Archived Driven, Damped Oscillator; Plot x(t)/A

    Homework Statement The problem is long so I will post the whole thing but ask only for help on part C. The steady-state motion of a damped oscillator driven by an applied force F0 cos(ωt) is given by xss(t) = A cos(ωt + φ). Consider the oscillator which is released from rest at t = 0...
  4. D

    No solution to harmonic oscillator

    Homework Statement Given (\mathcal{L} + k^2)y = \phi(x) with homogeneous boundary conditions y(0) = y(\ell) = 0 where \begin{align} y(x) & = \frac{2}{\ell}\sum_{n = 1}^{\infty} \frac{\sin(k_nx)}{k^2 - k_n^2},\\ \phi(x) & = \frac{2}{\ell}\sum_{n = 1}^{\infty}\sin(k_nx),\\ u_n(x) &=...
  5. D

    Generalized Green function of harmonic oscillator

    Homework Statement The generalized Green function is $$ G_g(x, x') = \sum_{n\neq m}\frac{u_n(x)u_n(x')}{k_m^2 - k_n^2}. $$ Show G_g satisfies the equation $$ (\mathcal{L} + k_m^2)G_g(x, x') = \delta(x - x') - u_m(x)u_m(x') $$ where \delta(x - x') = \frac{2}{\ell}\sum_{n =...
  6. D

    MHB Harmonic oscillator no solution

    Given \((\mathcal{L} + k^2)y = \phi(x)\) with homogeneous boundary conditions \(y(0) = y(\ell) = 0\) where \begin{align} y(x) & = \frac{2}{\ell}\sum_{n = 1}^{\infty} \frac{\sin(k_nx)}{k^2 - k_n^2},\\ \phi(x) & = \frac{2}{\ell}\sum_{n = 1}^{\infty}\sin(k_nx),\\ u_n(x) &=...
  7. A

    Exploring the Truths and Myths of the Harmonic Oscillator Model

    Homework Statement Which of the following statements about the harmonic oscillator (HO) is true? a) The depth of the potential energy surface is related to bond strength. b) The vibrational frequency increases with increasing quantum numbers. c) The HO model does not account for bond...
  8. K

    Fortran Fortran program for oscillator using Euler method

    I am trying to run a program with fortran. The program is about solving the Oscillator using Euler Method. I am trying to run this code and applying array arguments (as I want to extend it to 3 dimensions afterwards). When I try to compile, it comes up with an error "Unclassifiable statement at...
  9. M

    Forced Damped Oscillator frequency independent quantaties

    Homework Statement For the forced damped oscillator, show that the following are frequency independent. a) displacement amplitude at low frequencies. b) the velocity amplitude at velocity resonance. c) the acceleration amplitude at very high frequencies Homework Equations...
  10. M

    Archived Analyzing Power Absorption in a Lightly Damped Harmonic Oscillator

    Homework Statement For a lightly damped harmonic oscillator and driving frequencies close to the natural frequency \omega \approx \omega_{0}, show that the power absorbed is approximately proportional to \frac{\gamma^{2}/4}{\left(\omega_{0}-\omega\right)^{2}+\gamma^{2}/4} where \gamma is...
  11. O

    What is the physical meaning for a particle in harmonic oscillator ?

    For infinite square well, ψ(x) square is the probability to find a particle inside the square well. For hamornic oscillator, is that meant the particle behave like a spring? Why do we put the potential as 1/2 k(wx)^2 ? Thanks
  12. C

    Period of Harmonic Oscillator using Numerical Methods

    Homework Statement Numerically determine the period of oscillations for a harmonic oscillator using the Euler-Richardson algorithm. The equation of motion of the harmonic oscillator is described by the following: \frac{d^{2}}{dt^{2}} = - \omega^{2}_{0}x The initial conditions are x(t=0)=1...
  13. Astrum

    Quantum Harmonic Oscillator

    Homework Statement Compute ##\left \langle x^2 \right\rangle## for the states ##\psi _0## and ##\psi _1## by explicit integration. Homework Equations ##\xi\equiv \sqrt{\frac{m \omega}{\hbar}}x## ##α \equiv (\frac{m \omega}{\pi \hbar})^{1/4}## ##\psi _0 = α e^{\frac{\xi ^2}{2}}##The Attempt at...
  14. skate_nerd

    MHB ODE for a forced, undamped oscillator.

    I have a physics problem right now, and I am so close to finishing it... The problem is to consider an undamped (no friction) forced mass-spring system. The forcing is given by $$F(t)=F_o\cos{\omega_ft}$$ The general ODE for this would be $$\ddot{x}+(0)\dot{x}+\omega_o^2x=f_o\cos{\omega_ft}$$...
  15. S

    Using Generalization of Bohr Rule for 1D Harmonic Oscillator

    Homework Statement The generalization of the bohr rule to periodic motion more general than circular orbit states that: ∫p.dr = nh = 2∏nh(bar). the integral is a closed line integral and the "p" and "r" are vectors Using the generalized rule (the integral above), show that the spectrum for...
  16. G

    Modified Quantum Harmonic Oscillator

    This is more of a conceptual question and I have not had the knowledge to solve it. We're given a modified quantum harmonic oscillator. Its hamiltonian is H=\frac{P^{2}}{2m}+V(x) where V(x)=\frac{1}{2}m\omega^{2}x^{2} for x\geq0 and V(x)=\infty otherwise. I'm asked to justify in...
  17. D

    Differential Equation for a Wien Bridge Oscillator

    I am trying to write out a differential equation for the Wien bridge oscillator circuit. I have attached a picture of the circuit. I am considering ideal conditions. I am trying to solve for the output voltage but I need help setting up the differential equation.
  18. D

    Trouble with harmonic oscillator equation

    Consider the harmonic oscillator equation (with m=1), x''+bx'+kx=0 where b≥0 and k>0. Identify the regions in the relevant portion of the bk-plane where the corresponding system has similar phase portraits. I'm not sure exactly where to start with this one. Any ideas?
  19. H

    Eigenvalue for harmonic oscillator

    Homework Statement The Hamiltonian for a particle in a harmonic potential is given by \hat{H}=\frac{\hat{p}^2}{2m}+\frac{Kx^2}{2}, where K is the spring constant. Start with the trial wave function \psi(x)=exp(\frac{-x^2}{2a^2}) and solve the energy eigenvalue equation...
  20. M

    Harmonic Oscillator Problem: Consideration & Solutions

    Problem: Consider a harmonic oscillator of undamped frequency ω0 (= \sqrt{k/m}) and damping constant β (=b/(2m), where b is the coefficient of the viscous resistance force). a) Write the general solution for the motion of the position x(t) in terms of two arbitrary constants assuming an...
  21. AdrianHudson

    How Is Oscillation Frequency Calculated in a Parabolic Potential?

    Homework Statement consider a one dimensional parabolic potential of the form V(z) = 1/2π(√k/m) What is the oscillation frequency of this mass? Homework Equations 1/2π(√k/m) The Attempt at a Solution So here this is my attempt 1/2π(√10/.5) 1/2π(3.16/.5) 6.32(1/2π) =9.9 hz?
  22. T

    How does a simple oscillator work in non-ideal conditions?

    So I want to start off saying that I'm a senior in college in Electrical Engineering and I've been learning a lot about various kinds of circuits involving oscillators and I would like to know more about them. In school we talk a lot about them in various circuits and how important they are to...
  23. C

    Infinite energy states for an harmonic oscillator?

    So, I've read conference proceedings and they appear to talk about counter-intuitive it was to create an infinite-energy state for the harmonic oscillator with a normalizable wave function (i.e. a linear combination of eigenstates). How exactly could those even exist in the first place?
  24. AdrianHudson

    Frequency of a simple harmonic oscillator

    Homework Statement Consider a mass hanging from an ideal spring. Assume the mass is equal to 1 kg and the spring constant is 10 N/m. What is the characteristic frequency of this simple harmonic oscillator? Homework Equations No idea I think Hookes law F=-ky Some other relevant...
  25. L

    Simple Harmonic Oscillator Equation Solutions

    These are practice problems, not homework. Just wanting to check to see if my process and solutions are correct. 1. Given the following functions as solutions to a harmonic oscillator equation, find the frequency f correct to two significant figures: f(x) = e-3it f(x) = e-\frac{\pi}{2}it 2...
  26. F

    Q.M. harmonic oscillator spring constant goes to zero at t=0

    Homework Statement A one-dimensional harmonic oscillator is in the ground state. At t=0, the spring is cut. Find the wave-function with respect to space and time (ψ(x,t)). Note: At t=0 the spring constant (k) is reduced to zero. So, my question is mostly conceptual. Since the spring...
  27. S

    Periodically Dampened Oscillator

    Homework Statement A body with mass m is connected to a spring in 1D and is at rest at X = A > 0. For the region X > 0, the only force acting on the mass is the restoring force of the spring. For the region X < 0, a viscous fluid introduces damping into the system. a) Find the speed of the...
  28. jbrussell93

    Damped Oscillator homework

    Homework Statement A mass of 1000 kg drops from a height of 10 m on a platform of negligible mass. It is desired to design a spring and dashpot on which to mount the platform so that the platform will settle to a new equilibrium position 0.2 m below its original position as quickly as possible...
  29. N

    Solving Op-Amp Oscillator: Finding 3 dB Frequency and Maximum Gain

    Hi everyone, I was trying to solve this problem. Here at calculate 3 db frequency the gain should me 1/sqrt(2) times of the maximum voltage gain. So I calculated maximum gain which is 1+6/3=3 ( capacitor will be open for maximum gain). At 3db gain will be 3/1.414 3/1.414=(1+6k/(3k||(1/jwc)))...
  30. P

    Why is my sawtooth oscillator not oscillating?

    Hi Does anyone have an idea of why my oscillator doesn't oscillate? It's supposed to generate sawtooth. But the scope shows constant -13V. Actually the output of the oscillator has a more stable voltage than the input voltage source! It works IRL with ua741 opamp (but the 741 doesn't provide...
  31. M

    Noether theorem and scaling, ex.: 1-D Harmonic Oscillator

    Hello, if I think of the harmonic oscillator action S = ∫L dt, L = 1/2 (dx/dt)^2 - 1/2 x^2, and then of the "scaling transformation" x -> x' = 1/a x (a>0, const), then x = a x', and in new coordinates x', S' has the same form as in x except for multiplication by the constant a, formally...
  32. 6

    Understanding my crystal oscillator

    I have an obsolete, proprietary crystal oscillator. It is a 200MHz, 10 pin, SMT component. The number on the unit is 200N1. I cannot find another C.O. like it in size, number of pins or footprint. What I don't understand is 9 of the pins are grounded. Only one pin is used and it obviously puts...
  33. P

    Coupled Oscillator Homework: Normal Modes & Frequencies

    Homework Statement Two identical undamped oscillators, A and B, each of mass m and natural (angular) frequency $\omega_0$, are coupled in such a way that the coupling force exerted on A is \alpha m (\frac{d^2 x_A}{dt^2}), and the coupling force exerted on B is \alpha m (\frac{d^2...
  34. R

    Correlation function of damped harmonic oscillator

    The model of damped harmonic oscillator is given by the composite system with the hamiltonians ##H_S\equiv\hbar \omega_0 a^\dagger a##, ##H_R\equiv\sum_j\hbar\omega_jr_j^\dagger r_j##, and ##H_{SR}\equiv\sum_j\hbar(\kappa_j^*ar_j^\dagger+\kappa_ja^\dagger...
  35. D

    How do Sinusoidal output comes out in the Wein-Bridge Oscillator

    This question was asked to me in a VIVA. [b]What examiner asked. [b] How do Sinusoidal output comes out in the Wein-Bridge Oscillator. ... I tried to solve the problem using the control system. That is, by deriving the transfer function of the...
  36. S

    Poisson brackets for simple harmonic oscillator

    Homework Statement Considering the Hamiltonian for a harmonic oscillator: H=\frac{p^2}{2m}+\frac{mw^2}{2}q^2 We have seen that the equations of motion are significantly simplified using the canonical transformation defined by F_1(q,Q)=\frac{m}{2}wq^2cot(Q) Show explicitly that between both...
  37. D

    Putting phase factor in amplitude in Lorentz oscillator

    Hi there, In my course solid state physics, there is a part about the Lorentz oscillator. At a certain part, this is written: "X(t) = X_0sin(-ωt+α) This changes into: X(t) = X_0 exp(-iωt) by choosing X_0 as a complex number and putting the phase factor into the complex amplitude."...
  38. M

    Quantum Harmonic Oscillator necessary DE

    I was reading through my Principles of Quantum Mechanics textbook and arrived at the section that discusses the quantum harmonic oscillator. In this discussion the equation ψ"-(y^2)ψ=0 presents itself and a solution is given as ψ=(y^m)*e^((-y^2)/2), similar to a gaussian function i assume. My...
  39. R

    Quantum Resonant Harmonic Oscillator

    The Hamiltonian is ##H=\hbar \omega (a^\dagger a+b^\dagger b)+\hbar\kappa(a^\dagger b+ab^\dagger)## with commutation relations ##[a,a^\dagger]=1 \hspace{1 mm} and \hspace{1 mm}[b,b^\dagger]=1##. I want to calculate the Heisenberg equations of motion for a and b. Beginning with ##\dot...
  40. Tesladude

    Making an Oscillator Bomb with a 555 for Left4Dead

    Hi i use the 555 a lot and I am also a gamer. in the game "left4dead" they have a bomb that has an occilator to tell you when the bomb is going to go off bu blinking slowly at first, like 1hz then slowely increasing frequency up to maybe 10hz over somthing like a 10 second span. Does anyone...
  41. I

    Conservative overdamped harmonic oscillator?

    This isn't homework. I'm reviewing calculus and basic physics after many years of neglect. I want to show that a damped harmonic oscillator in one dimension is nonconservative. Given F = -kx - \small\muv, if F were conservative then there would exist P(x) such that \small -\frac{dP}{dx} = F...
  42. Rorshach

    3D harmonic oscillator- expected value of distance

    Homework Statement Hey! I got this problem about 3D harmonic oscillator, here it goes: A particle can move in three dimensions in a harmonic oscillator potential ##V(x,y,z)=\frac{1}{2}m\omega^2(x^2+y^2+z^2)##. Determine the ground state wave function. Check by explicitly counting that it is...
  43. fluidistic

    Ladder operator for harmonic oscillator, I don't get a mathematical

    If the ladder operator ##a=\sqrt {\frac{m\omega}{2\hbar}}x+\frac{ip}{\sqrt{2m\hbar \omega}}## and ##a^\dagger=\sqrt {\frac{m\omega}{2\hbar}}x-\frac{ip}{\sqrt{2m\hbar \omega}}## then I get that the number operator N, defined as ##a^\dagger a## is worth ##\frac{m \omega...
  44. C

    Quantum Harmonic oscillator, <T>/<V> ratio

    Homework Statement Consider an electron confined by a 1 dimensional harmonic potential given by ## V(x) = \dfrac{1}{2} m \omega^2 x^2##. At time t=0 the electron is prepared in the state \Psi (x,0) = \dfrac{1}{\sqrt{2}} \psi_0 (x) + \dfrac{1}{\sqrt{2}} \psi_4 (x) with ## \psi_n (x) = \left(...
  45. H

    Radiation from a charged harmonic oscillator

    Anyone know if there are any graphical simulations online for the field of a charged harmonic oscillator, or better yet maybe some kind of paper on it?
  46. E

    Harmonic oscillator problem

    Homework Statement consider a harmonic oscillator of mass m and angular frequency ω, at time t=0 the state if this oscillator is given by |ψ(0)>=c1|Y0> + c2|Y1> where |Y1> , |Y2> states are the ground state and the first state respectively find the normalization condition for |ψ(0)> and the...
  47. P

    3D harmonic oscillator orbital angular momentum

    Homework Statement i need to calculate the orbital angular momentum for 3D isotropic harmonic oscillator is the first excited state The Attempt at a Solution for the first excited state...
  48. Roodles01

    Particle in a potential well of harmonic oscillator

    Homework Statement I have a similar problem to this one on Physicsforum from a few years ago. Homework Equations Cleggy has finished part a) saying he gets the answer as Ψ(x, t) = (1/√2) (ψ1(x)exp(-3iwt/2+ iψ3(x)exp(-7iwt/2) OK classical angular frequency ω0 = √C/m for period of...
  49. fluidistic

    Probability, QM, harmonic oscillator, comparison with classical

    Homework Statement I must calculate the probability that the position of a harmonic oscillator in the fundamental state has a greater value that the amplitude of a classical harmonic oscillator of the same energy.Homework Equations ##\psi _0 (x)=\left ( \frac{m \omega}{\pi h } \right ) ^{1/4}...
  50. tomwilliam2

    Operators on a Harmonic oscillator ground state

    Homework Statement Calculate the expectation value for a harmonic oscillator in the ground state when operated on by the operator: $$AAAA\dagger A\dagger - AA\dagger A A\dagger + A\dagger A A A\dagger)$$ Homework Equations $$AA\dagger - A\dagger A = 1$$ I also know that an unequal number of...
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