Oscillator Definition and 1000 Threads

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...

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...

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...

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...

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...

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...

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...

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.

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...

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...

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...

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 =...

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

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...

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...

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...

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...

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!

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...

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...

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...

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...

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 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...