Oscillator Definition and 1000 Threads

Homework Statement Homework Equations Complex number solutions z= z0eαt Energy equations and Q (Quality Factor) The Attempt at a Solution For this question, I followed my book's "general solution" for dampened harmonic motions, where z= z0eαt, and then you can solve for α and eventually...

Homework Statement A particle is moving in a 1-dimensional harmonic osciallator with the hamiltion: ## H = \hbar \omega (a_+ a_- + \frac{1}{2})## at time ## t=0## the normalized wave function is given by ## \Psi(x,0) = \frac{1}{\sqrt{2}}(\psi_0(x) + i\psi_1(x)) ## Task: Calculate for ## t \geq...

Homework Statement A particle is moving in a one-dimensional harmonic oscillator, described by the Hamilton operator: H = \hbar \omega (a_+ a_- + \frac{1}{2}) at t = 0 we have \Psi(x,0) = \frac{1}{\sqrt{2}}(\psi_0(x)+i\psi_1(x)) Find the expectation value and variance of harmonic oscillator...

Homework Statement The amplitude of any oscillator can be doubled by: A. doubling only the initial displacement B. doubling only the initial speed C. doubling the initial displacement and halving the initial speed D. doubling the initial speed and halving the initial displacement E. doubling...

-If we have string of length L that has fixed ends, then we can easily find frequencies with which this string can oscillate: We just need to solve wave equation: ∂2y/∂x2=1/c2*∂2∂t2 (c is determined by strings properties (linear density and tension), with Dirichlet boundary conditions...

Homework Statement I have a project in university that's about creating a simplified model of a washing machine in the program ADAMs View. Here is a picture of how it's constructed: https://imgur.com/a/zZzS5 So basically to oversimplify the problem I've understood that the rotating mass will...

Homework Statement on page 51 (of my book, probably not current) section 2.3.2 equation 2.74 and 2.75 d2ψ / dξ2 ≈ ψξ2 Homework Equations This is an approximation of the Schrodinger equation with a variable introduced ξ = √(mω/h) The solution is given: ψ(ξ) = Ae-ξ2/2 +Beξ2/2The Attempt at...

Homework Statement An un-damped harmonic oscillator natural frequency ##\omega_0## is subjected to a driving force, $$F(t)=ame^{-bt}.$$ At time, ##t=0##, ##x=\dot{x}=0##. Find the equation of motion. Homework Equations ##F=m\ddot{x}## The Attempt at a Solution We have...

Homework Statement Consider an inertial laboratory frame S with coordinates (##\lambda##; ##x##). The Lagrangian for the relativistic harmonic oscillator in that frame is given by ##L =-mc\sqrt{\dot x^{\mu} \dot x_{\mu}} -\frac {1}{2} k(\Delta x)^2 \frac{\dot x^{0}}{c}## where ##x^0...

I have some difficulties in viewing the literature on the topic. In textbooks on analytical mechnics the procedure given for Special relativistic motion is to write the kinetic term relativistically and attach the unchanged potential term. So, for a harmonic oscillator the Lagrangian is ##L =...

Homework Statement [/B] For the first excited state of a Q.H.O., what is the probability of finding the particle in -0.2 < x < 0.2 Homework Equations Wavefunction for first excited state: Ψ= (√2) y e-y2/2 where: The Attempt at a Solution To find the probability, I tried the integral of...

Consider a spring-mass oscillator on a train moving at relativistic speed. According to SR, to a stationary observer, both the mass and the period will appear to have increased by a factor of γ. But the period is supposed to be proportional to the square root of the mass. Something is wrong...

1. Homework Statement I've been using a recurrence relation from "Adv. in Physics"1966 Nr.57 Vol 15 . The relation is : where Rnl are radial harmonic oscillator wave functions of form: The problem is that I can't prove the relation above with the form of Rnl given by the author(above). I've...

I'm currently studying IR but my mind is having trouble tying everything together. While I see that vibrational frequency is determined really by just reduced mass, I can see from the equation that vib equation is the same throughout energy levels and so does energy (bc that basically depends...

Homework Statement A spring with spring constant k is attached to a box of mass M in which is placed a small body of mass m. The system is displaced a distance A from equilibrium and released from rest. Find the normal force between the box and the small mass as a function of time. For what...

Homework Statement I don’t have a specific problem to solve, and I’m not sure I would be able to correctly find one, but I need to know how to solve a harmonic Oscilator problem with Friction. I believe I should be starting with F = -kx -Ff, and that I will be given some information about the...

See attached photo please. So, I don't get how equations of motion derived. Why is it that x dot is partial derivative of H in term of p but p dot is negative partial derivative of H in term of x.

Homework Statement Show that the virial theorem holds for all harmonic-oscillator states. The identity given in problem 5-10 is helpful. Homework Equations Identity given: ∫ξ2H2n(ξ)e-ξ2dξ = 2nn!(n+1/2)√pi P.S the ξ in the exponent should be raised to the 2nd power. So it should look like ξ2...

Homework Statement Show that application of the lowering Operator A- to the n=3 harmonic oscillator wavefunction leads to the result predicted by Equation (5.6.22). Homework Equations Equation (5.6.22): A-Ψn = -iΨn-1√n The Attempt at a Solution I began by saying what the answer should end...

I see this circuit has many applications for creating high voltage from a battery source in a very simple and compact manner. However, I’m not sure of the exact basis of oscillation - is it: 1. Current flows through FB, turns on transistor. 2. Primary induces opposing voltage in FB due to...

Homework Statement This is a question asked in a entrance examination[/B] A charged particle is in the ground state of a one-dimensional harmonic oscillator potential, generated by electrical means. If the power is suddenly switched off, so that the potential disappears, then, according to...

Homework Statement Homework EquationsThe Attempt at a Solution I tried differentiating both sides of 3 and re-arranging it such that it started to look like equation 2, however i got stuck with 2 first order terms z' and couldn't find a way to manipulate it into a function z. I then tried...

A harmonic function is one that satisfies Laplace's equation -- a definition cannot be more precise than that. However, in the study of vibrations, sine and cosine are considered harmonic functions; but they don't solve Laplace's equation. And then there are words like: harmonics (for higher...

If you consider b^2/m > 4*k, you can get the solution by using classic method (b = damping constant, m = mass and k = spring constant) otherwise you have to use complex numbers. How have the references books proved the solution for this differential equation?

Homework Statement An undamped harmonic oscillator (b=0) is subject to an applied force Focos(wt). Show that if w=wo, there is no steady- state solution. Find a particular solution by starting with a solution for w=wo+#, and passing to the limit #->0, it will blow up. Try starting with a...

Hi Q1: I was reading about ultraviolet catastrophe and it was said that atoms were assumed to be harmonic oscillators of radiation. I believe that two harmonic oscillators could have the same frequency but different amplitudes so it would mean that two different atoms (i.e. two harmonic...

(I list this as Advanced because the question is not what it seems from the title.) So most know the cases: no damping, underdamping, critical damping, overdamping. I got that: this is not a request for explanation. Rather... Does anyone know of a web page that has some tutorial ANIMATION...

I started to ponder following problem. I have a driven, damped oscillator where the mass is free to vibrate in y-direction. If I put a wall or a ground near the mass, the mass touches it if the drive amplitude is larger than the distance to the ground. How does this change the normal dynamics. I...

Hi everyone, I have a great doubt in this problem: Let a mass m with spin 1/2, subject to the following central potencial V(r): V(r)=1/2mω2r2 Find the constants of motion and the CSCO to solve the Hamiltonian? This is my doubt, I can't find the CSCO in this potencial. Is a problem in general...

Homework Statement In Griffiths' book "Introduction to Quantum Mechanics", Section 2.3, Chapter 2, the Fig. 2.7 gives the plots of the wave function (##\psi_{n}##) and its modulus of the harmonics oscillator, see the Appendix. With the order (##n##) increasing, they become both higher. However...

Homework Statement Hi everybody! In my quantum mechanics introductory course we were given an exercise about the 3D quantum harmonic oscillator. We are supposed to write the state ##l=2##, ##m=2## with energy ##E=\frac{7}{2}\hbar \omega## as a linear combination of Cartesian states...

Homework Statement With the Hamiltonian here: Compute the cananonical ensemble partition function given by ##\frac{1}{h} \int dq dp \exp^{-\beta(H(p,q)}## for 1-d , where ##h## is planks constant Homework EquationsThe Attempt at a Solution I am okay for the ##p^2/2m## term and the...

Homework Statement Consider a two-dimensional harmonic oscillator, described by the Hamiltonian ##\hat H_0 = \hbar \omega (\hat a_x \hat a_x ^{\dagger} + \hat a_y \hat a_y^{\dagger} + 1)## Calculate ##\hat H_0 \hat L | n_1, n_2 \rangle## and ##\hat L \hat H_0 |n_1, n_2 \rangle##. What does...

Homework Statement I am having issues with d) and would like to know if I did the a, b, and c correctly. I have tried to look online for explanation but with no success. A harmonic oscillator executes motion according to the equation x=(12.4cm)cos( (34.4 rad /s)t+ π/5 ) . a) Determine the...

Homework Statement The acceleration amplitude of a damped harmonic oscillator is given by $$A_{acc}(\omega) = \frac{QF_o}{m} \frac{\omega}{\omega _o} \sqrt{\it{R}(\omega)}$$ Show that as ##\lim_{\omega\to\infty}, A_{acc}(\omega) = \frac{F_o}{m}## Homework Equations $$\it{R}(\omega) =...

Homework Statement A simple harmonic oscillator has a potential energy V=1/2 kx^2. An additional potential term V = ax is added then, a) It is SHM with decreased frequency around a shifted equilibrium b) Motion is no longer SHM c)It is SHM with decreased frequency around a shifted equilibrium...

hi , i want to design a clapp oscillator with output frequency up to 150 MHZ , inductance value must be 0.24 u , who can help me please?? i need it for my project

Homework Statement Here is the equation for the general solution of an overdamped harmonic oscillator: x(t) = e-βt(C1eωt+C2e-ωt) Homework Equations β decay constant C1, C2 constants ω frequency t time The Attempt at a Solution I know (eωt+e-ωt)/2 = coshωt and (eωt-e-ωt)/2 = sinhωt but how do...

Homework Statement http://imgur.com/a/lv6Uo Homework Equations Look below The Attempt at a Solution I was unsure where to start. I thought that parseval's theorem may be helpful. I know the Potential energy is equivalent to .5kx^2 and T will be the integral of the force. So i have $$<E> =...

Homework Statement Find the first-order corrections to energy and the wavefunction, for a 1D harmonic oscillator which is linearly perturbed by ##H'=ax##. Homework Equations First-order correction to the energy is given by, ##E^{(1)}=\langle n|H'|n\rangle##, while first-order correction to the...

Homework Statement I have ##H'=ax^3+bx^4##, and wish to find the general perturbed wave-functions. Homework Equations First-order correction to the wave-function is given by, $$\psi_n^{(1)}=\Sigma_{m\neq n}\frac{\langle\psi_m^{(0)}|H'|\psi_n^{(0)}\rangle}{n-m}|\psi_m^{(0)}\rangle.$$ The...

I am a senior physics and mathematics major, and this is my last semester. As a result, I am taking advanced physics lab, which feels more like a grad school experiment than an undergrad. One of the labs deals with the modal analysis of three spring-mass systems placed vertically as shown in the...

Homework Statement Solve the Schrödinger Equation for an harmonic potential of the form (1/2)m\omega_+^2x^2 for x>0 and (1/2)m\omega_-^2x^2 for x<0. Find the equation that determines the energy spectrum. You can use m=1/2 and \hbar=1 Homework Equations [/B] I wrote down Schrödinger Equation...

Homework Statement Substitute \psi = Ne^{-ax^2} into the position-space energy eigenvalue equation and determine the value of the constant a that makes this function an eigenfunction. What is the corresponding energy eigenvalue? Homework Equations \frac{-\hbar^2}{2m}...

Hello, I'm studying the section 2.2 of "Introduction to Quantum Mechanics, 2nd edition" (Griffiths), and he shows this equation $$\frac{\partial^2\psi}{\partial x^2} = -k^2\psi , $$ where psi is a function only of x (this equation was derivated from the time-independent Schrödinger equation) and...

Homework Statement I am trying to follow a paper, https://arxiv.org/pdf/1410.0710v1.pdf, I want to get the results obtained in equations 5 and 6 but can't quite work out how eq 3 has been diagonalized. Homework Equations eq 3 The Attempt at a Solution As the system is driven i thought I'd...

Homework Statement [/B] What is the shortest time required for a harmonic oscillator to move from ##x = A## to ##x = \frac{A}{2}##? Express your answer in terms of the period ##T##. Homework Equations [/B] ##x(t)=Acos(\omega t)=Acos(2\pi\frac{t}{T})## The Attempt at a Solution ##A=Acos(0)##...

Homework Statement I got an alpha particle (charge 2+) fixed at x=0 and an electron fixed at x=2. I then add a fluor ion (charge 1-) to the right of the electron and we note his position xeq. The question is to find the constant spring (k) relative to the harmonic oscillation made by the fluor...

Homework Statement By Wien bridge oscillator (abbreviated as WBO below) I refer to this circuit where the op-amp is assumed to be ideal and the output is the voltage drained from the upper end of R3. What confuses me is that I hardly find a reference which explicitly states that a WBO has a...

Hi I am trying to run an RC oscillator using a 2N3904 (Datasheet for reference: http://www.kynix.com/uploadfiles/pdf8798/2N3904.pdf) The circuit looks like the following. I want to run it at 0-5v but I failed, I assume it is because the voltage is not high enough? What would you expect the...