Oscillator Definition and 1000 Threads

Hello The energy of harmonics oscillator, started of U=-\frac{\partial}{\partial \beta} \ln Z is equal to \frac{\hbar \omega}{2} + \frac{\hbar \omega}{exp(\beta \hbar \omega)-1}. At high temperature, i could say that exp (\beta \hbar \omega ) \approx 1 + (\beta \hbar \omega ), and then...

Homework Statement Okay, I am trying to solve this Anharmonic Oscillator equation. Now I am given with the potential U=(1/2)x^2-(1/4)x^4 and Kinetic energy T=(1/2)x' ^2 So the Lagrangian becomes \mathcal L=T-U Now I have taken all the k's and m to be 1 Homework Equations...

Homework Statement The question is from Sakurai 2nd edition, problem 3.21. (See attachments) ******* EDIT: Oops! Forgot to attach file! It should be there now.. *******The Attempt at a Solution Part a, I feel like I can do without too much of a problem, just re-write L as L=xp and then...

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...

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...

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...

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) &=...

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 =...

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) &=...

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...

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...

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...

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...

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

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...

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...

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 $$\ddot{x}+(0)\dot{x}+\omega_o^2x=f_o\cos{\omega_ft}$$...

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...

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...

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.

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?

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...

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...

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?

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...

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?

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...

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...

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...

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...

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...

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)))...

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...

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...

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...

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...

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...

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...

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...

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."...

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...

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...

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...

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...

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...

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...

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(...

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?

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...

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...