Oscillator Definition and 1000 Threads

We show by working backwards $$\hbar w \Big(a^{\dagger}a+\frac{1}{2}\Big)=\hbar w \Big(\frac{mw}{2\hbar}(\hat{x}+\frac{i}{mw}\hat{p})(\hat{x}-\frac{i}{mw}\hat{p})+\frac{1}{2}\Big)$$...

This is a BJT common collector colpitts oscillator.I have found how to find the feedback fraction from this site:http://fourier.eng.hmc.edu/e84/lectures/ch4/node12.html but I have searched for hours and haven't found the amplifier gain of this circuit. I have found the amplifier gain for...

So i have a rough sketch of a toothbrush with its main components. Its like an Oral B type of toothbrush with a DC motor i think...that uses some type of camshaft and gears to create a back and forth rotation of the head from the revolving motor. Theres a couple of components there that i don't...

This is the Colpitts oscillator: When we design a Colpitts oscillator we must set the value of C1 to be bigger than the parasitic capacitance of the emitter base junction. However in a Hartley oscillator we have an inductive voltage divider and I was wondering if we should put a big inductor...

I understand the masses will accelerate toward each other with the same varying speed before they reach the natural length of the spring. Then they continue to approach each other while compress the spring, that'll slow their speeds down definitely. So my question is, how could we calculate how...

First time posting in this part of the website, I apologize in advance if my formatting is off. This isn't quite a homework question so much as me trying to reason through the work in a way that quickly makes sense in my head. I am posting in hopes that someone can tell me if my reasoning is...

I don't get why the total mechanical energy is not conserved in this situation. When the length of the spring reaches the maximum, the speed of the block is 0 and we have the following equation: $$E=K+U=1/2mv^2+1/2kA^2,\text{where A is the amplitude} \implies E=1/2kx_{max}^2$$ I can't see why...

I'm having a hard time understanding how to treat fermions, bosons, and distinguishable particles differently for this problem. To the best of my understanding, I know that my overall state for bosons must be symmetric, and because they're spin-0, this means there's only one coupled spin state...

Hi everyone! Both sources I'm currently reading (page 291 of Mathematical Methods of Classical Mechanics by Arnol'd - get it here - and page 202 of Classical Mechanics by Shapiro - here) say that, in the case of the planar harmonic oscillator, using polar or cartesian coordinate systems leads...

hi guys i am trying to solve the Asymptotic differential equation of the Quantum Harmonic oscillator using power series method and i am kinda stuck : $$y'' = (x^{2}-ε)y$$ the asymptotic equation becomes : $$y'' ≈ x^{2}y$$ using the power series method ##y(x) = \sum_{0}^{∞} a_{n}x^{n}## , this...

I'm trying verify the proof of the sum rule for the one-dimensional harmonic oscillator: $$\sum_l^\infty (E_l-E_n)\ | \langle l \ |p| \ n \rangle |^2 = \frac {mh^2w^2}{2} $$ The exercise explicitly says to use laddle operators and to express $p$ with $$b=\sqrt{\frac {mw}{2 \hbar}}-\frac...

For the off-diagonal term, it is obvious that (p^2+q^2) returns 0 in the integration (##<m|p^2+q^2|n> = E<m|n> = 0##). However, (pq+qp) seems to give a complicated expression because of the complicated wavefunctions of a quantum harmonic oscillator. I wonder whether there is a good method to...

Hi, I'm watching a video about Hartley oscillator and I'm in trouble with a simple assumption: as stated at minute 5:50 if the two coils ##L_1## and ##L_2## are wound on the same core then taking into account the mutual inductance M he gets: ##L^ {'} _1 = L_1 + M## ##L^ {'} _2 = L_2 + M##...

Dear all, While simulating a coupled harmonic oscillator system, I encountered some puzzling results which I haven't been able to resolve. I was wondering if there is bug in my simulation or if I am interpreting results incorrectly. 1) In first case, take a simple harmonic oscillator system...

I just noticed something that is a little bit of a different perspective on a mass-on-spring (horizontal) simple (so undamped) oscillator's frequency and looking for some intuition on it. There are many ways to derive that for a mass on a horizontal frictionless surface on a spring with spring...

First of all, i tried to find w, the angular frequency, by calculating the oscillations from ta to tc, there is ~ 20 oscillations coursed. so, w = 2*pi*20/(tc-ta) ta = 0, tc = 0 + 5.2 ms And tried to find the factor gama y by A(t) = A*cos(Φ + wt)*e^(-yt/2) A(0) = 2.75u = A*cos(Φ) 1u = A*cos(Φ...

Too dim for this kind of combinatorics. Could anyone refer me to/ explain a general way of approaching these without having to think :D. Thanks.

Firstly, apologies for the latex as the preview option is not working for me. I will fix mistakes after posting. So for ##<x>## = (##\sqrt{\frac{\hbar}{2m\omega}}##) ##(< \alpha | a_{+} + a_{-}| \alpha >)## = (##\sqrt{\frac{\hbar}{2m\omega}}##) ##< a_{-} \alpha | \alpha> + <\alpha | a_{-}...

Can anyone help me find what is wrong in this circuit? given, slew rate of the op amp is 400V/us and max output current for opamp is 40mA but the opamp is lm741.

Hello folks, So the solution of the equation of motion for damped oscillation is as stated above. If we were to take an specific example such as: $$\frac{d^2x}{dt^2}+4\frac{dx}{dt}+5x=0$$ then the worked solution to the second order homogeneous is...

This is a question from an exercise I don't have the answers to. I have been trying to figure this out for a long time and don't know what to do after writing mx''¨(t)=−kx(t)+mg I figure that the frequency ω=√(k/m) since the mg term is constant and the kx term is the only term that changes. I...

I'm studying Ergodic Theory and I think I "got" the concept, but I need an example to verify it... Let's take the simplest possible 2D classical harmonic oscillator whose kinetic energy is $$T=\frac{\dot x^2}{2}+\frac{\dot y^2}{2}$$ and potential energy is $$U=\frac{ x^2}{2}+\frac{y^2}{2}$$...

Hello everybody, new here. Sorry in advance if I didn't follow a specific guideline to ask this. Anyways, I've got as a homework assignment two cannonical transformations (q,p)-->(Q,P). I have to obtain the hamiltonian of a harmonic oscillator, and then the new coordinates and the hamiltonian...

I've worked through it doing what I thought I should have done. I normalized the original wavefunction(x,0) and made it = one before using orthonormality to get to A^2(1-1) because i^2=-1 but my final answer comes out at 1/0 which is undefined and I don't see how that could be correct since A is...

Now, I once read in another thread here someone else was trying to make a kilohertz oscillator. The forum members said not to use a breadboard as it would create too much noise. So What do you recommend as an alternative? Or should I just connect the components without the foundation? Also...

Questions: 1. Is LM741 capable of oscillating at 10MHz? If not, could you suggest me an affordable op-amp for this operation? 2. How likely am I, as a beginner to be able to design a zero phase shift feedback filter to use with a non-inverting op-amp circuit to create an oscillator? 3. If an...

I am confused about the relation between the number state ##|n\rangle## with the annhilation and creation operators ##a^\dagger## and ##a## respectively, and the number of atoms in the harmonic oscillator. I'll try to express my current understanding, I thought the number states represent the...

Let's go step by step a) We know that the harmonic oscillator operators are $$a^{\dagger} = \frac{1}{\sqrt{2 \hbar m \omega}} ( -ip + m \omega q)$$ $$a= \frac{1}{\sqrt{2 \hbar m \omega}} (ip + m \omega q)$$ But these do not depend on ##L##, so I guess these are not the expressions we want...

So in my textbook on oscillations, it says that angular frequency can be defined for a damped oscillator. The formula is given by: Angular Frequency = 2π/(2T), where T is the time between adjacent zero x-axis crossings. In this case, the angular frequency has meaning for a given time period...

I was studying the ##n##-dimensional harmonic oscillator, whose Hamiltonian is $$\hat H = \sum_{j=1}^{n} \Big( \frac{1}{2m} \hat p_j^2 + \frac{\omega^2 m}{2} \hat q_j^2 \Big)$$ The ladder operators are $$a_{\pm} = \frac{1}{\sqrt{2 \hbar m \omega}} ( \mp ip + m \omega q)$$ And came across an...

Hi! As I outlined in my https://www.physicsforums.com/threads/hello-reality-anyone-familiar-with-the-davisson-germer-experiment.985063/post-6305937, I'm curious to ask if there is anyone with knowledge on the theory of the piezoelectric effect on this forum? I think it's fascinating how a...

c = Critically Damped factor c = 2√(km) c = 2 × √(150 × .58) = 18.65 Friction force = -cv Velocity v = disp/time = .05/3.5 Friction force = - 18.65 * .05/3.5 = -.27 N I am not sure if above is correct. Please check and let me know how to do it.

Hi everyone 🙂 I have read this article about the arc converter, also known as the Poulcen arc. https://en.m.wikipedia.org/wiki/Arc_converter It was apparently one of the first electric oscillators. Apparently, an electric arc was produced between two electrodes to put in resonance a RLC...

I know that ahat_+ = 1/sqrt((2*m*h_bar*w)) * (mw(xhat)+i(phat)) and ahat_- = 1/sqrt((2*m*h_bar*w)) * (mw(xhat)-i(phat)). But I'm not sure what (ahat_+)^+ could be.

I found the steady state solution as F_0(mw_0^2 - w^2m)Coswt/(mwy)^2 + (mw_0^2 -w^2m)^2 + F_0mwySinwt/(mwy)^2 + (mw_0^2 -w^2m)^2 But I'm not sure how to sketch the amplitude and phase? Do I need any extra equations?

I don't quite understand how he got the line below. By using discrete time approximation, we can get the second order time expression. But i don't see how by combining terms he is able to get such expression.

My question also applies to the damped driven oscillator, however for simplicity I will first consider an undamped oscillator. The equation of motion is $$-kx + F_{0} \cos{\omega t} = m \ddot{x}$$ or in a more convenient form $$\ddot{x} + {\omega_{0}} ^{2}x = \frac{F_{0}}{m} \cos{\omega t}$$The...

I'm working through https://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-fall-2013/lecture-notes/MIT8_05F13_Chap_06.pdf, and I'm stumped how they got from Equation 5.26 (##\vert 0_{\gamma} \rangle \equiv \frac{1}{\sqrt{cosh\gamma}} exp(-\frac{1}{2}tanh\gamma \hat{a^\dagger}\hat{a^\dagger}...

I can show that ##\frac{d}{dt} \langle \psi (t) \vert X^2 \vert \psi (t) \rangle = \frac{1}{m} \langle \psi (t) \vert PX+XP \vert \psi (t) \rangle##. Taking another derivative with respect to time of this, I get ##\frac{d^2}{dt^2} \langle \psi (t) \vert X^2 \vert \psi (t) \rangle = \frac{i}{m...

I am currently having trouble deriving the volume element for the first octant of an isotropic 3D harmonic oscillator. I know the answer I should get is $$dV=\frac{1}{2}k^{2}dk$$. What I currently have is $$dxdydz=dV$$ and $$k=x+y+z. But from that point on, I'm stuck. Any hints or reference...

An electric field E(t) (such that E(t) → 0 fast enough as t → −∞) is incident on a charged (q) harmonic oscillator (ω) in the x direction, which gives rise to an added ”potential energy” V (x, t) = −qxE(t). This whole problem is one-dimensional. (a) Using first-order time dependent perturbation...

Hi, I am studying Wireless Energy Transfer and I find Royer Oscillator in that. Ref: Wikipedia https://en.wikipedia.org/wiki/Royer_oscillator I am unable to understand how it works. I found a diagram here: Ref: https://www.smps.us/inverters.html It says that (quoted from webstie): In practice...

In the paper below I've seen a new method to solve the quantum harmonic oscillator Introduction to the Spectrum of N=4 SYM and the Quantum Spectral Curve It is done using the concept of quasi momentum defined as $$p = - i \frac{d(\log \psi)}{dx}$$ See pg 7,8 Is this well know? is it discussed...

I posted yesterday but figured it out; however, a different issue I just detected with the same code arose: namely, why does the solution damp here for an undamped simple harmonic oscillator? I know the exact solution is ##\cos (5\sqrt 2 t)##. global delta alpha beta gamma OMEG delta =...

Dear PF community, I am back with a question :) The solutions for the quantum harmonic oscillator can be found by solving the Schrödinger's equation with: Hψ = -hbar/2m d²/dx² ψ + ½mω²x² ψ = Eψ Solving the differential equation with ψ=C exp(-αx²/2) gives: -hbar/2m (-α + α²x²)ψ + ½mω²x²ψ = Eψ...

The wavefunction is Ψ(x,t) ----> Ψ(λx,t) What are the effects on <T> (av Kinetic energy) and V (potential energy) in terms of λ? From ## \frac {h^2}{2m} \frac {\partial^2\psi(x,t)}{\partial x^2} + V(x,t)\psi(x,t)=E\psi(x,t) ## if we replace x by ## \lambda x ## then it becomes ## \frac...

Hey, I solved a problem about a double pendulum and got 2 euler-lagrange equations: 1) x''+y''+g/r*x=0 2) x''+y'' +g/r*y=0 (where x is actually a tetha and y=phi) the '' stand for the 2nd derivation after t, so you can see the basic harmonic oscillator equation with a term x'' or y'' that...

I'm not sure how will this oscillator work. Assume A is low, so B will be high and the capacitor will charge through B-C- 2Mohm. Now even D has gone high, so A will be high and B will be low and C will discharge. I'm not sure how the voltage divider rule across RC will take into effect. I found...