Oscillator Definition and 1000 Threads

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...

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...

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...

It is known to all that the Hamiltonin H=p^2/m+x^2 can describe the boson and fermion particle, but how can embody the fermion properties when a fermion oscillator interacted with a boson oscillator? what is their interaction form?

Why the reciprocal of the damping rate in this model equal to the phonon lifetime? Can somebody give me a detailed exaplanation. Thanks.

Hi there, I just started an intermediate classical mechanics course at university and was smacked upside the head with this question that I don't know how to even start. Homework Statement We are to find the response function of a damped harmonic oscillator given a Forcing function. The...

I am thinking of using the output frequency of a 555 relaxation oscillator for measurement purposes. The frequency would be related to my measurement signal. How stable are these oscillators at low frequencies? Any personal experiences would help. How stable can you get then with good...

Homework Statement The period of a macroscopic pendulum made with a mass of 10 g suspended from a massless cord 50 cm long is 1.42 s. (a) Compute the ground state (zero-point) energy. (b) If the pendulum is set into motion so that the mass raises 0.1 mm above its equilibrium position, what will...

Homework Statement http://img191.imageshack.us/i/questionyw.png/ Homework Equations Given in problem The Attempt at a Solution a) I've been able to find expressions of operators x, p_x, y and p_y in terms of the creation/annihilation operators and hence been able to express the...

i have a quick question A particle in ground state of a S.H.O whose potential is given by V_1(X)=\frac{1}{2}mw^2_1x^2 suddenly changes to V_2(X)=\frac{1}{2}mw^2_2(x-x_o)^2 what is the wavefunction going to be like for the new potential? i'd think everything else stays the same in the...

Hello, I want to find <xftf|x(t)|xiti> in harmonic oscillator. I tried to insert the complete set of energy eigenstates to the right and the left side of x(t), but it yields somewhat more complicated stuff. Thank you

Homework Statement a block of mass m=.5kg is sliding on a horizontal table with coefficients of static and kinetic friction of .8 and .5 respectively. It is attached to a wall with a spring of unstretched length l=.13m and force constant 200 n/m. The block is released from rest at t=0 when...

Homework Statement There is a block attached to the wall via a spring. The only damping force is friction, where there is kinetic and static. Homework Equations m(d^2x/dt^2)=-kx-? The Attempt at a Solution I can solve this, except usually the damping force is given as...

Homework Statement I'm talking about the probability density plot of the harmonic oscillator. Is there some physical meaning to be extracted from this? Here's a link that contains the drawing of what I'm talking about http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hosc5.html...

Homework Statement The problem can be found here. http://wopho.org/dl.php?id=17&dirfile=selection-problem/helical_rope.pdf" I am attempting to solve part 3. Homework Equations The Lagrangian of the system is: L= \frac{m\dot{x}^2}{2}+\frac{mr^2\dot{\theta}^2}{2}-k \left(...

Homework Statement The question states for a harmonic oscillator the wavefunction is: \mu = C*x*exp(-\alphax2/2) it then wants you to find \alpha. using the standard hamiltonian: H = -\hbar/2m d2/dx2 + 1/2 mw2x2 I have differentiated \mu twice and put it into the TISE. for the left hand...

Homework Statement A particle is in the ground state of a harmonic oscillator with classical frequency w. Suddenly the classical frequency doubles, w -> w' = 2w without initially changing the wavefunction. Instantaneously afterwards, what is the probability that a measurement of energy...

Homework Statement A harmonic oscillator starts in its ground state (n=0) at t=-infinity. A perturbation H = -xF(t) is applied between t= -infinity and t = T. (a) by considering the corresponding classical interaction explain why this represents the application of a time dependent force...

Homework Statement We know that a particle in SHM is in a state such that measurements of the energy will yield either E_0 or E_1 (and nothing else), each with equal probability. Show that the state must be of the form \psi = \frac{1}{\sqrt2} \psi_0 + \frac{e^{i \phi}}{\sqrt2} \psi_1 where...

Homework Statement Hi guys. I've been working on this problem for a while, it's starting to frustrate me. "Show that the function of Ѱ=e^(-bx^2) with b=mw/2ħ is a solution and that the corresponding energy is ħw/2." Homework Equations Schrodinger Eqn...

Hi can anybody explain to me how to calculate values for the resonant tank of the clapp oscillator. I know that capacitor in series with inductor sets the frequency. But I ve read that formula 1/Ceq = 1/c1+1/c2+ 1/cs, should be used to get Ceq which should be used for frequency setting. So what...

Homework Statement In the time interval (t + δt, t) the Hamiltonian H of some system varies in such a way that |H|ψi>| remains finite. Show that under these circumstances |ψi> is a continuous function of time. A harmonic oscillator with frequency ω is in its ground state when the stiffness of...

Is it necessary that force term in anharmonic oscillator should contain only third power in dependent variable(say x)? or any other higher power in dependent variable.

In the attached file, I have formulated a simple one dimensional harmonic oscillator and solved the model numerically. Such a model might represent a simple reaction coordinate along which a liquid drop actinide nucleus might split after absorbing a neutron. Clearly the complete model involves...

Hi, I've got a few questions about that common base colpitts oscillator. I am trying to simulate it but, I am not sure if the circuit is complete or is it missing anything? I have some formulas but not sure how to use them.I have some assumptions, are they right? 1. Capacitors R3 R4 nad R5...

I have designed an opamp based on thfollowing square wave setup http://www.national.com/ds/LM/LM124.pdf on page 11. I want to know what i would have to adjust to lower the frequency to the range of 10 hertz, it has a 5 volt input and the frequency range is at 10 Ghz I believe. any help would...

Pleae help me. a),b),c) was already solved. but question d) is not.

Hi, could anyone explain to me what the purpose of the each capacitor is in this common base colpitts?. C1,C1,L are used to set the oscillation frequancy, right? R1, R2,R3 are used to set the collector, base current and volatges, is that correct? So what is the purpose of C3, C5 and C4...

uncertainty relation. I think I'm on the right track. Currently, I'm at, E = (1/2m)*<p^2> + (1/2)*k*<x^2> and when applying the uncertainty relation, deltax = <x^2>^(1/2) deltap = <p^2>^(1/2) How do I go about connecting everything from here? Thanks!

Homework Statement A particle of mass m that is confined to a harmonic oscillator potential V(x) = \frac{1}{2} m \omega^2 x^2 is described by a wave packet having the probability density, |\Psi (x,t) |^2 = \left(\frac{m\omega}{\pi\hbar} \right )^{1/2}\textrm{exp}\left[-\frac{mw}{\hbar}(x -...

Homework Statement Verify that the ground state (n=0) wavefunction is an eigenstate of the harmonic oscillator Hamiltonian. Using the explicit wavefunction of the ground state to calculate the average potential energy <0|\hat{v}|0> and average kinetic energy <0|\hat{T}| 0> Homework...

1. Homework Statement Show that bohr's hypothesis (that a particle's angular momentum must be an integer multiple of h/2pi) when applied to the three dimensional harmonic oscillator, predicts energy levels E=lh/pi w with l = 1,2,3. Is there an experiment that would falsify this prediction...

The TISE can be written as -\frac{\hbar^{2}}{2m}\frac{d^{2}u}{dx^{2}} + \frac{1}{2}m\omega_{0}^{2}x^{2}u = Eu Now my lecture notes say that it is convenient to define scaled variables y = \sqrt{\frac{m\omega_{0}}{\hbar} x} and \alpha = \frac{2E}{\hbar\omega_{0}} Hence \frac{d}{dx} =...

Homework Statement In a reservoir there are three balls. There is a spring(the weight of spring is negligible) with elastic coefficient k between each two balls(small enough, like two particles). Suppose the center of gravity of the system does not move, and the mass of each ball is m. Suppose...