Oscillator Definition and 1000 Threads

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...

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>...

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 =...

Homework Statement For the Harmonic Oscillator, the state |ψ> = (|0> + |1>) / √(2) Find \overline{x} = <ψ|x|ψ> \overline{p} = <ψ|p|ψ> \overline{x^2} = <ψ|x^{2}|ψ> and \overline{p^2} = <ψ|p^{2}|ψ> and <ψ| (x - \overline{x})^2 |ψ><ψ| (p - \overline{p})^2 |ψ> [b]2. Homework Equations...

Hello, I am confused about how to show that any two solutions of the damped harmonic oscillator equation equal another solution. Thanks!

This is an assignment for a class titled "Intro to Scientific Programming" and it is a prerequisite for Computational Physics. Homework Statement Create a graph of the position of a damped oscillator as a function of time.Homework Equations The equation is x = A*e^((-b/2m)*t)cos(omega*t +...

hay guys, A three-dimensional harmonic oscillator is in thermal equilibrium with a temperature reservoir at temperature T. Finde The average total energy of the oscillator I have no idea, how can I solve this problem, can you hint me please:rolleyes:

hi, i'm trying to see how does an HO, traveling with constant speed v looks like. suppose a unitless system H = P^2+(X-vt)^2 define Y = X-vt then H = P^2+Y^2 i can see that [P,Y] = -i (unitless - no h-bar) so i guess it means that P and Y are conjugate space/momentum operators...

Consider the usual 1D quantum harmonic oscillator with the typical hamiltonian in P and X and with the usual ladder operators defined. i) I have to prove that given a generic wave function \psi , \partial_t < \psi (t) |a| \psi (t)> is proportional to < \psi (t) | a | \psi (t) > and...

Homework Statement The problem statement is given in its entirety in the attachment. 2. Homework Equations / 3. The Attempt at a Solution Unfortunately, I have no clue where to start. :( I should add that due to extenuating circumstances I've missed quite a bit of physics instruction...

Homework Statement Consider a damped oscillator Assume that the mass is 318g, the spring constant is 104 N/m, and b = 0.106 kg/s. How long does it take for the amplitude to drop to half its initial value? M = 318 g Or 0.318 kg K = 104 N/m b = 0.106 kg/s Homework Equations n / a The...

Hello, If I understand correctly, the main contribution inside solids that result in the behavior of a black body at high temperatures is that the electron clouds vibrate around their nuclei. Please correct me if I'm wrong. If I'm correct: to get a black body spectrum every frequency...

Homework Statement A particle of mass m is placed in the ground state of a one-dimensional harmonic oscillator potential of the form V(x)=1/2 kx2 where the stiffness constant k can be varied externally. The ground state wavefunction has the form ψ(x)\propto exp(−ax2\sqrt{k}) where a...

Homework Statement Consider critically damped harmonic oscillator, driven by a force F(t) Find the green's function G(t,t') such that x(t) = ∫ dt' G(t,t')F(t') from 0 to T solves the equation of motion with x(0) =0 and x(T) =0Homework Equations x(t) = ∫ dt' G(t,t')F(t') from 0 to TThe Attempt...

Well what is the partition function of harmonic oscillator with this energy E=hw(n+1/2) , n=1,3,5,... Z=e^(-BE) right? B=1/KT^2 How to expand this? Thank you.

Homework Statement The circuit in attached figure behaves as an oscillator. What is the oscillation amplitude? 2. The attempt at a solution With H(s), I've calculated the oscillation condition: KM \geq L_1+L_2, and the oscillation frequency: \omega = R_1/\sqrt(L_1 L_1 - M^2) How can I...

Hi. I want to write the entropy of a 1d harmonic oscillator as a function of energy, but for each energy there is only one possible configuration. So is the entropy zero? I mean, the energy is E=hw(n+1/2), so there is only one microstate for each energy.

Homework Statement What are the stationary states of an isotropic 3D quantum harmonic oscillator in a potential U(x,y,z) = {1\over2}m\omega^2 (x^2+y^2+z^2) in the form \psi(x,y,z)=f(x)g(y)h(z) and how many linearly independent states have energy E=({3\over 2}+n)\hbar\omega? Homework...

Homework Statement A non-linear oscillator consisting of a mass on a spring has a potential energy of the form \frac{1}{2}kx^2 - \frac{1}{3}\alpha x^3, where k and \alpha are positive constants, and x is displacement. Using conservation of energy, show that the motion is oscillatory if the...

Homework Statement A spring is elastically stretched 10 cm if a force of 3 Newtons is imposed. A 2 kg mass is hung from the spring and is also attached to a viscous damper that exerts a restraining force of 3 Newtons when the velocity of the mass is 5 m/sec. An external force time function...

Hi, I'm trying to resolve a problem (17-2) of Pauling's book (Introduction to Quantum Mechanics ), but I'm not achieving this integration. So, I ask for your help. The problem says: Calculate \overline{p_{z}²} (where p_{z} = momentum in z direction and \overline{x} = average value of x...

Homework Statement Let's consider a harmonic oscillator with a harmonic perturbation: H = \frac{p^2}{2} + \frac{x^2}{2} + a \frac{x^2}{2}. Exact solution is known, but we want to derive it using perturbation theory. More specifically, suppose we want to obtain a series for the ground state...

How are Hermite Polynomials related to the solutions to the Schrodinger equation for a harmonic oscillator? Are they the solutions themselves, or are the solutions to the equation the product of a Hermite polynomial and an exponential function? Thanks!

Homework Statement Consider a capacitor consisting of two metal plates with a charge +Q on one plate and −Q on the other. In the gap of the capacitor we have two perfectly harmonic springs attached to the top plate—one with a H atom and the other with a H ion attached to the end of the...

Homework Statement http://www.circuitstoday.com/colpitts-oscillator Homework Equations Dear Members, Kindly go through this link. I read Capacitors block DC then how can the supply voltage Vcc which is essentially DC can charge the capacitors of the tank circuit? Kindly help members...

A mechanical oscillator connected to the end of a stretched string creates a transverse displacement of the end that is given by ξ = 0.009 sin(22.8 t), where ξ is in meters, t is in seconds (and the argument of the sin function is in radians). The tension in the string is 11.08, and the string...

Hello: I am trying to understand how to build a hamiltonian for a general system and figure it is best to start with a simple system (e.g. a harmonic oscillator) first before moving on to a more abstract understanding. My end goal is to understand them enough so that I can move to symplectic...

The book derives the wavefunction for the ground state of a harmonic oscillator. It's found to be a Gaussian with dispersion l = \sqrt{\frac{\hbar}{2m\omega}}. The probability distribution for momentum is found to be Gaussian as well with dispersion \sigma_{p} = \frac{\hbar}{2l}. The following...

Homework Statement my spreadsheet: (oh and please ignore the fact that I've got my amplitude set to 39, i was still answering question 1 when i took the screen shot) the question i am currently having problems with is question 2: Homework Equations i know the potential is...

the general solution is given by x(t) = Acos(ωt) + Bsin(ωt). Express the total energy in terms of A and B and notice how it is independent of time. my book derives a formula earlier which says \frac{\partial{S_{cl}}}{\partial{t_f}} = -E where S_{cl} is the classical path defined by S_{cl} =...

Hello everyone. I understand that a phase shift oscillator works by connecting an amplifier through a feedback network that shifts the input by 180 degrees. Although I remembered building a phase shift oscillator in my circuits class using an omp amp, I would like to build one using a bjt...

I found via this forum the hint to use the inverse squared equation to differentiate to find the resonance frequency from the amplitude equation (equilibrium not transient solution). Thank you! (AlephZero?) When substituting the resulting frequency for the resonance into the amplitude...

The position of the center of the box shown is given by the equation: x = 4.4 m * cos(29/sec * t) (a) What is the position of the box 2 seconds after the oscillations have started? x = m I don't know how to start A. I plugged in 2 seconds for t in the above equation, but my answer...

Have any of you seen the Expert village you tube vids? I saw that they only explain how to build a square wave Oscillator. Do any of you know of a simple circuit that will creat an adjustable sign wave? I have been through many circuits and had success in learning from project kits. I know...

Homework Statement Compute the partition function Z = Tr(Exp(-βH)) and then the average number of particles in a quantum state <nα > for an assembly of identical simple harmonic oscillators. The Hamiltonian is: H = \sum _{k}[(nk+1/2)\hbar - \mu nk] with nk=ak+ak. Do the calculations once...

Homework Statement If the damping constant of a free oscillator is given by b=2 m ω0, the oscillator is said to be critically damped. Show by direct substitution that in this case the motion is given by x=(A+Bt)e^(−βt) where A and B are constants. A critically damped oscillator is at...

Homework Statement The equation for a damped oscillator is d2x/dt2+2βdx/dt +ω02 x = 0. Let ω0=1.0 s−1 and β = 0.54 s−1. The initial values are x(0) = x0 and v(0)=0. Determine x(t)/x0 at t = 2π/ω0. Homework Equations the solution to equation is given by...

Homework Statement The logarithmic decrement δ of a lightly damped oscillator is defined to be the natural logarithm of the ratio of successive maximum displacements (in the same direction) of a free damped oscillator. That is, δ = ln(An/An+1) where An is the maximum displacement of the n-th...

Homework Statement The logarithmic decrement δ of a lightly damped oscillator is defined to be the natural logarithm of the ratio of successive maximum displacements (in the same direction) of a free damped oscillator. That is, δ = ln(An/An+1) where An is the maximum displacement of the n-th...

Homework Statement A damped harmonic oscillator is being forced. I have to say whether it is direct forcing or forcing by displacement. I have the equation of motion which is expressed in terms of the particle's height above the equilibrium point and an expression for the force being...

Hi ! There's a lot of information about Harmonic Oscillator.But I'm just a beginner of physics.And my English is not excellent to understand all informations in the Internet.Is there anybody,who can explain me Harmonic Oscillator?

Homework Statement Please take a look at the attachment for the problem statement. Homework Equations For 1 dim Harmonic oscillator, E = (n+1/2)h.omega/2pi I don't know which equation to use for 2 dim The Attempt at a Solution I am unable to solve because I don't know which...

Homework Statement Kindly look at the attachment for the statement. Homework Equations L^2 (psi) = E (psi) The Attempt at a Solution For Part B, I wrote Lx, Ly, Lz in operator form. Thus I get L^2. L^2 (psi) = E (psi) psi = E^-alpha.r^2/2 So I get energy eigenvalue 2 h cross...

Hi I'm having problems with solving this question: a 90.0 kg skydiver hanging from a parachute bounces up and down with a period of 1.50 seconds. What is the new period of oscillation when a second skydiver, whose mass is 60.0 kg, hangs from the legs first? the answer is 1.94 seconds...

I'm sorry if the form of my post does not meet the general requirements(this is the first time i work with any kind of LaTeX) and I promise that my next posts will be more adequate. Right now I am in serious need of someone explaining me this problem, since on the 6th of June I'm supposed to...

I'm solving the 2D harmonic oscillator, numerically. -\frac{1}{2}\left( u_{xx} + u_{yy}\right) + \frac{1}{2}(x^2+y^2)u = Eu The solutions my solver spits out for say, the |01> state, are linear combinations of the form |u\rangle = \alpha_1 |01\rangle + \alpha_2 |10\rangle which is...

Homework Statement Folks, I am looking at a past exam question regarding the Harmonic Oscillator. The question ask 'Justify that the ground state of a harmonic oscillator a_\psi_0=0 equation 2.58 on page 45 of griffiths. THis was not covered in my notes. Any ideas how to justify this...

Homework Statement Greetings, gents. I have a modelization problem you might be able to help me with... I have two oscillators, modeled as: osc_{1}=\cos{(a z)}osc_{2}=\cos{(\frac{b}{z})} and a resonance condition f(z) when these two oscillators are combined, modeled as...

Can someone please explain to me in layman's terms what a non-linear oscillator is? I need to determine if a ring pendulum is a non-linear oscillator, but I can't really do that without knowing what it is I am describing.

In a damped forced harmonic oscillator the amplitude is determined by a series of paramenters according to : A = (Fo/m)/ (sqrt( (wo^2-w^2)^2+(wy)^2) ). where Fo= driving force, m=mass of spring wo=natural frequency of system. w=driving frequency y=damping constant. Now my...