Oscillator Definition and 1000 Threads

I mean its part of the equation. 1/2 x k x xm x e^-bt/m for mechanical energy

I thinking of high Q oscillator examples* and pondered planetary orbits. The oscillators I am familiar with all shift energy either from place to place or different forms (mass-spring, L-C, E-B, etc.). But a planet in orbit (let's say circular) has potential and kinetic energy that never really...

My inductor has 8 turns, 4 cm diameter and 4 cm length. The capacitor I use is a 1 microfarad polyester capacitor. When the copper wire inductor is connected to DC voltage the compass needle is deflected by 90 degrees and the multimeter detects 1 A or 1000 mA of current. When DC is switched...

Reference textbook “The Physics of Waves” in MIT website: https://ocw.mit.edu/courses/8-03sc-...es-fall-2016/resources/mit8_03scf16_textbook/ Chapter 2 - Problem 2.2 [Page 51] (see attached file) Question: In the content of Page 43 (see attached file), it also states that the amplitude of...

The problem and solution is, However, I am confused how they get ##\vec a = (1, 2)## (I convert from column vector to coordinate form of vector). I got ##\vec a = (a_1, a_2) = (a_1, 2a_1) = a_1(1, 2)## however, why did they eliminate the constant ##a_1##? Thanks for any help!

I've tried to solve this problem (Zettili, Exercise 3.5) four times at this point. I believe my equation for the wave function at a later time ##t## is correct. The problem is my continuity equation is not satisfied; it does not equal zero. It's close but I'm off by a factor of ##m## and...

I purchased this vibration generator to construct a Chladni plate. I was hoping to use it with my existing oscilloscope (which appears to be very old). It seems the oscilloscope is not giving me a signal strong enough to drive the generator. Any suggestions for a different amplifier or power...

Hi, I had those exercises and want to know if they're correct. Also, feedback/tips would be great from you, professionals. $$A$$ 1. Let's consider the oscillator with a friction parameter... \begin{equation} m \ddot{x}+\alpha \dot{x}=-\kappa x \end{equation} but with \begin{equation}...

I don't understand what the question means, and the answer is provided here: https://physics.stackexchange.com/a/35821/222321 Could someone provide a comprehensive one-by-one explanation.

I am wondering if it is possible to use two electromagnets oscillating at about 1 ghz to suspend an amount of ferrofluid in an acrylic chamber. As I understand it, 1 ghz should be sufficient enough to get the ferrofluid away from each magnet, as after a quick google search, magnetic fields move...

Hello. I have tried to solve it using x-t Graph. We know that period of this function is ##T=\frac {1}{6}s##. Then I've used ##x(t)=0## to find the times in which the oscillator is at ##x=0##: ##t=\frac {k}{12} + \frac {1}{24}## for ## k \in Z.## Now I can draw x-t graph. We should check time...

First i looked at the case of ## \epsilon = 0## and came to the conclusion, that this oscillator has a circular limit cycle in a phase space trajectory, when plotted with the axes x and ##\dot{x}##. I have found that ##x_0^p (t) = a_1 \cos(t)## which implies that all other Fourier- coefficients...

Let's say I know the position space wavefunctions of the 1d harmonic oscillator ##\psi_n(x)## corresponding to the state ##| n \rangle## are known. I want to write ##\psi_m(x + a)##, for fixed ##m = 1,2,...##, in terms of all of the ##\psi_n(x)##. I know \begin{align*} \psi_n(x+a) = \langle x |...

Same instruction was given while finding value of 'g' by a bar pendulum. In the former case,does the spring obeys hooke's law while it forms a coupled harmonic oscillator system?Does the bar pendulum somehow breaks the simple harmonic motion(such that we can't apply the law for sumple harmonic...

What is the oscillator model in a generalized Snyder scheme？How to derive the formula？

For this problem, The solution is, However, can someone please explain how this is showing equation 15.35 as a solution of equation 15.34? I though both sides should be equal without assuming that ##\phi = 90## Also why are they allowed to assume ##\phi = 90##? Many thanks!

I was assuming there could be something via perturbation theory? I am unsure.

This is an equation I found for the delta phase lag of a driven oscillator. W is the driving angular frequency and Wo is the natural angular frequency of the driven system. Of course this is just a small part of the solution to the differential equation. Now ... 1) when W is much smaller than Wo...

The book(Schaum) says the above is the solution but after two hours of tedious checking and rechecking I get 2n^2 in place or the 3n^2. Am I missing something or is this just a typo?

Consider the equation of motion for a simple harmonic oscillator: ##m\ddot {x}(t)=-kx(t).## The solutions are ##x(t)=Ae^{i\omega t}+Be^{-i\omega t},## where ##\omega=\sqrt{\frac{k}{m}}##, and constants ##A## and ##B##. Physically, what does it mean for a solution to be complex? Is it only the...

Hi, I have been thinking about pendulums a bit and discovered that a HO(harmonic Oscillator) will take the same time to complete one period T no matter which amplitude A/length l it has, if stiffness k and mass m are the same. But moving on to a simple pendulum suddenly the time period for one...

I have a little doubt about Morse potential used for vibration levels of diatomic molecules. With regard to the image below, if the diatomic molecule is in the vibrational ground state, when the oscillation reaches the maximum amplitude for that state the velocity of the molecule must be zero so...

I just encountered an RF cavity in the wild for the first time. It was used as the frequency reference in the Agilent 8640B RF signal generator, which I believe dates back to the 70's. Were quartz oscillators not an option back then? Or were they worse in stability back then? I'm curious about...

Hi. I have attached a neatly done solution to the above question. I request someone to please check my solution and help me rectify any possible mistakes that I may have made.

Hello, So about two weeks ago in class we looked at RLC circuits in our E&M course, and short story short... we compared the exchange of energy between the Capacitor and the Inductor (both ideal) to simple harmonic motion. Once the capacitor and inductor are not ideal anymore, we said it's...

I need to know if I have solved the following problem well: A spin-less particle of mass m is confined to move on the surface of a cylinder of infinite height with a harmonic potential on the z-axis and Hamiltonian ##H=\frac{p_z^2}{2m}+\frac{L_z^2}{2mR^2}+\frac{1}{2}m\omega^2z^2## and I need to...

Hello there, I am trying to solve the above and I'm thinking that the solutions will be Hermite polynomials multiplied by a decaying exponential, much like the standard harmonic oscillator problem. The new Hamiltonian would be like so: $$H = - \frac \hbar {2m} \frac {d^2}{dx^2}\psi + \frac...

I thought I would multiply b to the whole equation of T, but I have no idea how to formulate into the type of solution it wants

Khan Academy claims that a simple pendulum not a perfect simple harmonic oscillator. Why is it so?

##x## can be discretized as ##x \rightarrow x_k ## such that ##x_{k + 1} = x_k + dx## with a positive integer ##k##. Throughout we may assume that ##dx## is finite, albeit tiny. By applying the Taylor expansion of the wavefunction ##\psi_n(x_{k+1})## and ##\psi_n(x_{k-1})##, we can quickly...

Hi, I have to find the eigenvalues and eigenvectors for a system of 3 masses and 4 springs. At the end I don't get the right eigenvalues, but honestly I don't know why. Everything seems fine for me. I spent the day to look where is my error, but I really don't know. ##m_a = m_b = m_c## I got...

I found ## \frac{\gamma}{2} = 7##, ##\gamma = 14## ##\omega_0^2 = \omega_d^2 + \frac{\gamma^2}{4} = 25## ##\omega_0 = \omega = 25##, thus ##\delta = \frac{\pi}{2}## ##A = \frac{\frac{F_0}{m}}{\sqrt((\omega_0^2 - \omega^2)+ \gamma^2\omega^2)} = 0.04## Thus, ##X(t) = 0.04sin(25t + \frac{\pi}{3} -...

yeah, I don't even know how to start

I want to create an LC circuit with varying inductors and compare those inductors for efficiency. Would it be accurate to suggest measuring the area under the curve of the first cycle of the resonant frequency would determine which of the inductors are most efficient? If the area is greater...

What I already know In general, power gain is desirable for an oscillator in order to make up for the losses and then feedback that gain (amplified signal) into the oscillator for it to keep oscillating. Voltage gain is not generally used for oscillators. What I want to know Since power gain is...

It is possible to build a purely passive RC phase shift oscillator with 2 separate (in the future) RC stages like this? Where there would be 2 RC networks that each provide 180 degrees of phase shift. Of course, there would be a buffer in between the 2 RC networks so that they behave as 2...

There are some articles from the 1980s where the authors discuss 1D quantum oscillators where ##V(x)## has higher than quadratic terms in it but an exact solution can still be found. One example is in this link: https://iopscience.iop.org/article/10.1088/0305-4470/14/9/001 Has anyone tried to...

Hello everyone. I am having some trouble with an RC phase shift oscillator that I built as a hobby project. I am completely stuck on this and I just cannot figure it out. My oscillator is not oscillating. Here is the circuit that I am trying to get to work. Taken from...

1. Since N is large, ignore the kinetic energy term. ##[-\mu + V(r) + U|\Psi (r)|^2]\Psi (r) = 0## 2. Solve for the density ##|\Psi (r)|^2## ##|\Psi (r)|^2 = \frac{\mu - V(r)}{U}## 3. Integrate density times volume to get number of bosons ##\int|\Psi (r)|^2 d\tau = \int \frac{\mu -...

Can I create a nonlinear spring, for a nonlinear oscillator, by putting many linear springs in series and parallel?

Summary:: I am trying to find the exact ground state energy of the hamiltonian.kindly help me with this

I just want to check if my thinking is reasonable. Since B,C and D are all dependent or fixed by the oscillator, A is the only factor to affect the amplitude of the motion at resonance or even throughout the entire process?

There is an mass-spring oscillator made of a spring with stiffness k and a block of mass m. The block is affected by a friction given by the equation: $$F_f = -k_f N tanh(\frac{v}{v_c})$$ ##k_f## - friction coefficient N - normal force ##v_c## - velocity tolerance. At the time ##t=0s##...

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Hello! Is stimulated emission possible for a harmonic oscillator (HO) i.e. you send a quanta of light at the right energy, and you end up with 2 quantas and the HO one energy level lower (as you would have in a 2 level system, like an atom)?

Consider the gaussian kick potential, ##\hat{V}(t) = \hat{x} \exp{(\frac{-t^2}{2 \tau^2})}## where ##\hat{x} = a+a^\dagger## in terms of creation and annihilation operators. Then we define the potential in the interaction picture, ##\hat{V}_I(t) = e^{i\hat{H}t}\hat{V}(t)e^{-i\hat{H}t}## I...

Good afternoon all, On page 51 of David Griffith's 'Introduction to Quantum Mechanics', 2nd ed., there's a discussion involving the alternate method to getting at the energy levels of the harmonic oscillator. I'm filling in all the steps between the equations on my own, and I have a question...

Consider a one-dimensional harmonic oscillator. ##\psi_0(x)## and ##\psi_1(x)## are the normalized ground state and the first excited states. \begin{equation} \psi_0(x)=\Big(\frac{m\omega}{\pi\hbar}\Big)^{\frac{1}{4}}e^{\frac{-m\omega}{2\hbar}x^2} \end{equation} \begin{equation}...

the differential equation that describes a damped Harmonic oscillator is: $$\ddot x + 2\gamma \dot x + {\omega}^2x = 0$$ where ##\gamma## and ##\omega## are constants. we can solve this homogeneous linear differential equation by guessing ##x(t) = Ae^{\alpha t}## from which we get the condition...