Oscillator Definition and 1000 Threads

It is well known that for an isolated system, the normal mode frequency of a N-body harmonic oscillator satisfies Det(T-\omega^{2}V)=0. How about a non-isolated, fixed temperature system? In solid state physics I have learned that in crystal the frequency does not change, but the amplitude of...

So, today while doing my homework for statistical mechanics I was reading about the quantum linear oscillator in the textbook, "Classical and Statistical Thermodynamics" by Ashley H. Carter. In it, after discussing the quantized energy it says: "Note that the energies are equally spaced and...

Homework Statement A particle mass m in the harmonic oscillator potential starts out in the state \psi(x,0)=A\left(1-2\sqrt(\frac{m\omega}{\hbar})x\right)^{2}e^{\frac{-m\omega}{2\hbar}x^{2}} for some constant A. a) What is the expectation value of the energy? b) At some time later T the wave...

Homework Statement A particle in the ground state of the harmonic oscillator with classical frequency \omega, when the spring const quadruples (so \omega^{'}=2\omega) without initially changing the wave function. What is the probability that a measurement of the energy would still return the...

Homework Statement A critically damped oscillator with natural frequency \omega starts out at position x_0>0. What is the maximum initial speed (directed towards the origin) it can have and not cross the origin? Homework Equations For the case of critical damping...

http://img707.imageshack.us/i/electronicsoscillator.jpg/ Dont know where to start for showing voltage difference at input is zero, suspose its something to do with non idealities of the op amp? For the oscillator question , kinda know how its works; there's positive saturation giving...

Homework Statement The pendulum of a grandfather clock has a period of 1s and makes excursions of 3cm either side of dead centre. Given that the bob weighs 0.2kg, around what value of n would you expect its non negligible quantum amplitudes to cluster? Homework Equations [/B] The...

Hi! Info: This is a rather elementary question about the creation a(+) and annihilation (a-) operators for the 1D H.O. The problem is to calculate the energy shift for a given state if the weak perturbation is proportional to x⁴. Using first order perturbation theory for the...

i am a last year EE student and I am creating a library in simulink. and at 1 stage i need to simulate a ring oscillator . i ve done it but with a lil bit of problems in the simulations. I am using spice parameters for simulink . that's why i asked if any of you guys have done it before. how do...

Hello (this is not a homework) I have a doubt about the ring oscillator. I have to create a R.O. with a frequency of 10kHz, now I know i have to link an odd number of inverters in a ring form, but using the formula of (f=1/2*n*Tp) it gives me a frequency in the Megas, I've red you can use a...

Homework Statement Two masses attached via springs (see picture attachment). k_n represents the spring constant of the n^{th} spring, x_n represents the displacement from the natural length of the spring. There are two masses, m_1 and m_2.2. The attempt at a solution My problem is formulating...

Homework Statement I need to find the time constant, tau, Homework Equations WILL EDIT THIS TOMORROW Bleeping FMS giving me major brainache *saddest face ever* A(t) = A_0 times e^-t/tauThe Attempt at a Solution I have had numerous attempts and I just fried my (fibromyalgic) brain out with...

Hello, Attached are two problems I can not solve, thanks for the help. The Attempt at a Solution For the first question, I understand that I need insert A1coswt+A2sinwt into the homogenous equation , but don't know what's then .. But I'm pretty much lost on both of em :(

Homework Statement Ok so the question is, is the state u(x) = Bxe^[(x^2)/2] an energy eigenstate of the system with V(x) = 1/2*K*X^2 and what is the probability per unit length of this state.Homework Equations The Attempt at a Solution So the way i did this was, to find if the state is an...

A particle of mass m moves along the x-direction such that V(x)=½Kx^2. Is the state u(¥)=B¥exp(+¥2/2), where ¥ is Hx (H = constant), an energy eigenstate of the system?. What is probability per unit length for measuring the particle at position x=0 at t=t0>0?

Homework Statement Given that a^+|n\rangle=\sqrt{n+1}|n+1\rangle a|n\rangle=\sqrt{n}|n-1\rangle and that the other eigenstates |n> are given by |n\rangle=\frac{(a^+)^n}{\sqrt{n!}}|0\rangle where |0> is the lowest eigenstate. Define for each complex number z the coherent state...

In my high school calculus-based electricity class two students and I are trying to create a demo where we set up a parallel plate capacitor and have some dielectric material inside it that we can pull out slightly, and have it oscillate into and out of the capacitor. Some ideas we have...

Imagine a fictitious universe where springs want to stretch: the spring force is proportional to, and in the same direction as, displacement from equilibrium. We'll call these anti-springs. (a) Set up a differential equation modeling the motion of a damped anti-spring if the mass is m = 1 kg...

Homework Statement Given the Hamiltonian for the harmonic oscillator H=\frac{p^2}{2m}+\frac{1}{2}m\omega^2 x^2 , and [x,p]=i\hbar . Define the operators a=\frac{ip+m\omega x}{\sqrt{2m\hbar \omega}} and a^+=\frac{-ip+m\omega x}{\sqrt{2m\hbar \omega}} (1) show that [a,a^+]=1 and that...

I am doing a discrete event simulation of logic gates and I have come upon a problem. I have set up a system similar to a ring oscillator. I understand that this system should not oscillate, but after thinking about it, I'm not sure why not. The system has one input, 1 fed into a NAND gate. The...

If an oscillator were to ever reach the visible spectrum, would an antenna connected with the oscillator output generate light?

My answer would be "yes," and here's my argument: If we let H = -\frac{\hbar^2}{2m} \frac{\partial^2}{\partial x^2} + \frac 12 m \omega^2 x^2, it is a Hermitian operator with familiar normalized eigenfunctions \phi_n(x) (these are products of Hermite polynomials and gaussians) and associated...

Hi, I don't understand why the momentum probability distribution of the quantum mechanical oscillator has the same shape as the position probability distribution (with peaks at the extremes), I mean, I understand the mathematics but I don't understand the concept. This is my reasoning (which...

I am trying to build something but I’m too stupid to understand this stuff so I need some help. Basically I am trying to create a system that will produce a constant sine wave, frequency of somewhere between 420 – 440 hertz under water with the greatest amount of amp output possible. I...

Homework Statement Show that G(q_2,q_1;t)=\mathcal{N}\frac{e^{iS_{lc}}}{\sqrt{\det A}} where \mathcal{N} is a normalization factor independent of q1, q2, t, and w. Using the known case of w=0, write a formula for G such that there is no unknown normalization factor. Homework Equations I...

With regards to this http://www.electronics-tutorials.ws/waveforms/555_oscillator.html, I figured out how to get t2 fine, but I have a problem figuring out how to get t1...I know when the negative-going waveform at pin 2 crosses Vcc/3, pin 3 goes to Vcc, and pin 7 gets internally disconnected...

Homework Statement Consider a particle of mass m moving in a 3D-anisotropic oscillator potential: V(\vec{r}) = \frac{1}{2}m(\omega^{2}_{x}x^{2}+\omega^{2}_{y}y^{2}+\omega^{2}_{z}z^{2}). (a) Frind the stationary states for this potential and their respective energies. Homework Equations...

Homework Statement What is the probability that a particle in the ground state of a simple harmonic oscillator 1-D potential will be found outside the region accessible classically Homework Equations ∫(between 1 and infinity) e^(-y^2 ) dy=0.08π^(1/2) I feel like it's quite a...

Homework Statement A particle is moving in a simple harmonic oscillator potential V(x)=1/2*K*x^2 for x\geq0, but with an infinite potential barrier at x=0 (the paddle ball potential). Calculate the allowed wave functions and corresponding energies.Homework Equations I am thinking that the...

For part of my lab write up on pendulum motion, my professor wanted us to find out why a pendulum was not a simple harmonic oscillator, and under what conditions it was. He also wanted to show this mathematically. So far what I have is that if there is no damping(friction?) and if the the...

Homework Statement Given a simple pendulum with a mass on the end and a massless string. The support point for the pendulum is moved laterally with an amplitude D at the resonant frequency. The damping is from the air and is considered viscous i.e. not turbulent. The difference between the...

Homework Statement The wave function \psi_0 (x) = A e^{- \dfrac{x^2}{2L^2}} represents the ground-state of a harmonic oscillator. (a) Show that \psi_1 (x) = L \dfrac{d}{dx} \psi_0 (x) is also a solution of Schrödinger's equation. (b) What is the energy of this new state? (c) From a look at...

Hi, I have a question about damped oscillator. Actually, although I have read courses about oscillator, I couldn't solve this. I think this is very easy question :( 1. Homework Statement Consider the solution for the damped ( but not driven ) oscillator, x =...

Tuning forks are lightly damped SHO's. Consider a tuning fork who's natural frequency is f=392Hz. Angular frequency = w = 2(Pi)f = 2463 (rad/s) The damping of this tuning fork is such that, after 10 sec, it's amplitude is 10% of it's original amplitude. Here is my attempt to find the damping...

Homework Statement For a particle of mass m moving in the potential V(x) = \frac{1}{2}m\omega^2x^2 (i.e. a harmonic oscillator), it is often convenient to express the position and momentum operators in terms of the ladder operators a_{\pm}: x = \sqrt{\frac{\hbar}{2m\omega}}(a_+ + a_-) p =...

I need to build a circuit and it requires Maxim's MAX2623 VCO. I need to mod my circuit so the frequency the VCO would run from 850 to 2100 MHz. Maxim doesn't supply or make such, but Crystek does. I found Crystek CVCO55BES-0950-2050, which runs at 950 to 2050 MHz. This is good enough since...

Dear All I want to design a 1MHz sine wave oscillator to be used as carrier wave for Amplitude Modulation. Which will be the best approach in terms of frequency and amplitude stability and why? Can the technique be implement using high slew rate op amp and also can we use crystal...

If I have mass on a spring that is oscillating in a linear motion, this system has a certain energy. Now if we imagine the system to be aligned along the vertical, why is the energy lower when gravity is turned on? I can calculate it and see that it is correct, but what is the "explanation" ...

Hi, I'm currently working through some exam papers from previous years before an upcoming module in Quantum Mechanics. Homework Statement See the attached image Homework Equations The Attempt at a Solution I'm a little stumped with this one, I'm assuming that I'm looking...

I need someone to please verify my work. Homework Statement A particle of mass m is suspended from the ceiling by a spring of constant k and initially relaxed length l_0. The particle is then let go from rest with the spring initially relaxed. Taking the z-axis as vertically oriented...

Homework Statement A body of mass 4[kgr] is moving along the x-axis while the following force is applied on it: F= -3(x-6) We know that at time t=0 the kinetic energy is K=2.16[J] and that its decreasing, that is, \frac{dK}{dt}<0 . The potential energy (with respect to the equilibrium...

Homework Statement Having a unidemsional array of N oscillators with same frequency w and with an anharmonic factor ax^4 where 0 < a << 1 Calculate, up to the first order of a, the partition function. Homework Equations For one oscillator...

I've looked at a few introductory treatments of the quantum harmonic oscillator and they all show how one arrives at the discrete energy values E_n = ( \frac {1}{2} + n ) hf \hspace {10 mm} n=0,1,2... usually by setting up and then solving the Schrodinger equation for the system...

Homework Statement How does change acceleration of relativistic linear harmonic oscillator with distance of equilibrium point in laboratory reference system? Homework Equations The Attempt at a Solution x=x_0sin(\omega t+\varphi) \upsilon=\omega x_0cos(\omega...

Homework Statement \omega_{x} = \omega \omega_{y} = \omega + \epsilon where 0 < \epsilon<<\omega Question: Find the path equation. Homework Equations I started with the 2D equations: x(t) = A_{x}cos(\omega_{x}t + \phi_{x}) y(t) = A_{y}cos(\omega_{y}t + \phi_{y}) The Attempt at a Solution...

Is there any loss of energy of a particel (electron) while getting collission with the walls of a finite square/rectangular barrier? since there is a enormous no. of collision a particle takes.

A classical harmonic oscillator follows a smooth, sinusoidal path of oscillation. Since on a quantum level energy levels are discrete, does a quantum harmonic oscillator actually oscillate in the everyday sense?

Hello there, Can anyone help me, I am struggling with solving LHO in two dimension,but in the polar coordinates. I transfer laplacian into polar from decart coordinates, write Ψ=ΦR, and do Fourier separation method for solving differential equation. But I do not know how to solve...

Hi all, I am having trouble with a certain integral, which I got from Quantum Physics by Le Bellac: \int dxdp\;\delta\left( E - \frac{p^2}{2m} - \frac{1}{2}m\omega^2x^2 \right) f(E) The answer to this integral should be 2\pi / \omega\; f(E) . My attempts so far: This integral is basically a...

Hello guys. This is not really a homework exercise, but I'm currently preparing for an exam and this is a question I got from a textbook. I'm currently sort of stuck, but here are the details. Homework Statement Link to a scan of the problem...