Oscillator Definition and 1000 Threads

Homework Statement Just click the link, The image is huge, so I did not use IMG tags. http://i.imgur.com/zWNRf.jpg Homework Equations Let's see, The rotational kinetic energy of a body is given as K = \frac{1}{2}Iω^{2} for a point mass, I = mr^{2} for a rigid rod rotating at it's end...

Homework Statement A mass m is attached to a spring of stiffness k. The spring is attached to the ceiling and the mass hangs freely from the spring under the force of gravity. (a) Derive the equation of motion for this system. (b) Find an expression for the equilibrium position of the...

At classical harmonic oscillator, total energy is proportional to square of frequency, but at quantum harmonic oscillator, total energy is proportional to frequency. Are those two frequencies the same? How it is with transition from quantum harmonic oscillator to classical harmonic oscillator...

Hoping someone can help me with some basic questions about resistor-capacitor oscillator (timer) circuits. I can put them together, I see them working, but I don't understand why! In the circuit in the attached drawing, if one installs the correct values of resistor and capacitor, I know...

Hello, I have this problem with deriving the formule from de definition of potential energy Picture show a mass-spring system in rest position: In general potential energy can be written as dot product: \frac{dE_{P}}{d\overrightarrow{y}}=-\overrightarrow{F}. Potential energy wil...

Homework Statement Consider a damped oscillator, with natural frequency ω_naut and damping constant both fixed, that is driven by a force F(t)=F_naut*cos(ωt). a) Find the rate P(t) at which F(t) does work and show that the average (P)avg over any number of complete cycles is mβω2A2. b)...

Hi,I am currently doing my project of designing a 100Mhz Voltage controlled oscillator,but i am stucked in the oscillator part,can anyone tell me about the oscillator between the feedback model method and negative resistance method?how to identify the result of my oscillator is work by using ADS?

I have a question regarding an oscillator design from a controls perspective. An ideal harmonic oscillator has just 2 poles, both on the imaginary axis, and their location along the axis determines the frequency of oscillation as well as the amplitude. Now, please correct me if this is...

Homework Statement I'm looking at the 1d harmonic oscillator \begin{equation} V(x)=\frac{1}{2}kx^2 \end{equation} with eigenstates n and the time dependent perturbation \begin{equation} H'(t)=qx^3\frac{(\tau^2}{t^2+\tau^2} \end{equation} For t=-∞ the oscillator is in the groundstate...

Homework Statement Sinusoidal driving force driving a damped oscillator (mass = m). Natural frequency is assumed to equal the drive frequency = w Time has elapsed to the point any transients have dissipated. Show that the energy dissipated by the damping force [F=-bv] during one cycle is...

So I was just thinking about regenerative braking, piezoelectric sensors/strain gauges, magnetic-induced currents etc. and I thought of a question that would make a simple/decent discussion/practice in general engineer/physics (lots of /'s) Suppose you have a simple harmonic oscillator :: WALL...

Let's say I have a 2D harmonic oscillator: Homework Statement The potential is of course defined by: V = 1/2m(Omegax)x^2 + 1/2m(Omegay)y^2 Homework Equations Generally when doing a harmonic oscillator we find that in two dimensions the energy is just: (Nx+Ny+1)hbarOmega is the energy. How...

Homework Statement I showed earlier this semester that in the presence of a "constant force", F_{o}, i.e. V=-Fx, that the eigenvalues for the Harmonic oscillator are shifted by \frac{F^{2}}{2m\omega^{2}} from the "unperturbed" case. It was also discussed that x\rightarrow...

Homework Statement Using the normalization constant A and the value of a, evaluate the probability to find an oscillator in the ground state beyond the classical turning points ±x0. Assume an electron bound to an atomic-sized region (x0 = 0.1 nm) with an effective force constant of 1.0...

I'm not understanding the following formula. I'm a computer programmer and was given a set of formulas to have an application to solve; however I'm not completely understanding how this works. I'm just looking for a step by step way to solve this and an explanation on why there are 3 assignment...

Homework Statement You are told that, at the known positions x_{1} and x_{2}, an oscillating mass m has speed v_{1} and v_{2}. What are the amplitude and angular frequency of the oscillations? Homework Equations x(t) = Acos(wt - \delta) v(t) = -Awsin(wt -\delta) w =...

The problem given is a perturbation on the two dimensional harmonic oscillator where the perturbation is simply: H'=-qfy. It seems that all of the elements of the matrix H' are zero and so constructing a diagonal matrix in the subspace is eluding me. Any ideas?

Ok here's the question: A body m is attached to a spring with spring constant k. While the body executes oscillations it also experiences a damping force F = -βv where 'v' is time derivative of displacement of the body from its equilibrium position. I believe equation of motion is F =...

Hey guys, For a particular problem I have to determine the total degeneracy across N 3-D Quantum Harmonic oscillators. Given that the degree of degeneracy for a 3-D harmonic oscillator is given by: (n+1)(n+2)/2 and the Total energy of N 3d quantum harmonic oscillators is given by...

My last attempt at building a simple oscillator did not go so well. After doing research on harmonic electronic oscillators, I finally came across one that seemed relatively simple (not a whole lot of parts) and that had an easily computed resonance frequency, the Clapp oscillator. I have...

For a harmonic oscillator with mass M, spring of stiffness k and displacement the force equation is: -kx = Md2x/dt2 How do you handle the situation and work out a solution for x(t) when the mass has an initial velocity. E.g. a mass dropped onto the spring?

Homework Statement Relate the frequency of a harmonic oscillator (spring) to that of a simple harmonic oscillator (pendulum) Show all derivations. Homework Equations pendulum: f=(1/(2∏))√(g/L) The Attempt at a Solution Not exactly sure how to go about this...is it saying...

Homework Statement Given damping constant b, mass m spring constant k, in a damped driven oscillation system the average power introduced into the system equals the average power drained out of the system by the damping force, for what values of ω does the instantanious damping power =...

Problem: Consider a harmonic oscillator of mass m undergoing harmonic motion in two dimensions x and y. The potential energy is given by V(x,y) = (1/2)kxx2 + (1/2)kyy2. (a) Write down the expression for the Hamiltonian operator for such a system. (b) What is the general expression for...

I have a question if i have a oscillator pushing 7.8 Hz 144 Hz cycle top (polarity 288 Hz) 432 Hz bottom cycle ... What kind oscillator is this?

Hello everybody, recently in my quantum mechanical course we were introduced to the concept of the quantum harmonic oscillator. My question is: is there a physical significance attached to the fact that the classical turning points overlap with the sign change of the second derivative of the...

I am creating an experiment to show how wireless energy can be transferred through resonantly tuned lc circuits. In order for this to work i need an oscillator. I have been told to try a colpitts oscillator. I have looked online and found a few sites showing calculators and schematics for these...

How can we tell whether a given v0 will cause an oscillator to overshoot the equilibrium? If the velocity high enough, we know the oscillator will overshoot and return to equilibrium. But if v0 is low, the system would act like it came from a point a bit farther out and not overshoot (right?)...

Hi, In one of my advanced quantum mechanics classes, the instructor posed a problem, namely to show that the ground state of a one dimensional quantum harmonic oscillator is unique, without getting into differential equations. I know that the equation a\left|0\right\rangle = 0 when...

Homework Statement An underdamped harmonic oscillator with mass m, spring constant k, and damping resistance c is subject to an applied force F0cosωt. (a) [analytical] If, at t = 0, x = x0 and v = v0, what is x(t)? Homework Equations Ωinitial = √(k/m) The Attempt at a...

What is the normalized ground-state energy eigenfunction for the three-dimensional harmonic oscillator V(r) = 1/2 m* ω^2 * r^2 Use separation of varaibles strategy. Express the wave function in spherical coordinates. What is the orbital angualar momentum of the ground state? Explain? I...

Homework Statement A mass of 1000 kg drops from a height of 10.0 m onto a platform of negligible mass. It is desired to design a spring and damper on which to mount the platform so that it will settle to a new equilibrium position 2.00 m below its original position as quickly as possible...

Homework Statement A harmonic oscillator with a vertical mass on a string has a hanging mass of 2m and a spring constant of K. It oscillates with an amplitude of Z. When its position is at a distance Z/2 of the equilibrium point, its potential energy is Ui. What is the maximum kinetic energy...

Homework Statement Damping is negligible for a 0.139 kg mass hanging from a light 7.00 N/m spring. The system is driven by a force oscillating with an amplitude of 1.88 N. At what frequency will the force make the mass vibrate with an amplitude of 0.430 m? There are two possible solutions...

Cheers everybody, the Hamiltonian of an even anharmonic oscillator is defined as H_N(g) = - \frac{1}{2} ∂_q^2 + \frac{1}{2} q^2 + g q^N (N even). In a paper (PRl 102, 011601) I found that to determine the eigenenergies of this system the Euclidean path integral formalism is used. They...

I recently designed a circuit of VCO and obtained a plot for frequency v/s Vc(control voltage). The graph was pretty much linear for a certain range of Vc but tends to become non linear when Vc is further increased or decreased. How do I explain the non linearity...?? The schematic of...

Homework Statement Show that the underdamped oscillator solution can be expressed as x(t)=x_{0}e^{-γt}[cos(Ω't+((v_{o}+γx_{o})/(x_{o}Ω')sinΩ't] and demonstrate by direct calculation that x(0)=x_{o} and \dot{x}(0)=v_{o} Homework Equations The underdamped oscillator solution is...

In the context of normal modes, what is a free mode? When the whole system is in motion?

Homework Statement I was wondering if there was a general method for finding a function that fits a set of data for a damped harmonic oscillator I'm currently writing up a presentation on the experiment for the gravitational constant and the way i did the experiment was to use a torsion...

Homework Statement A simple harmonic oscillator with mass m = 1/2 and k = 2 is initially at the point x = √3 when it is projected towards the origin with speed 2. Find the equation of motion describing x(t). Homework Equations x=Asin(ωt+θ) The Attempt at a Solution At t=0...

1. Homework Statement [/b] Consider the damped oscillator illustrated in the figure below. Assume that the mass is 365g, the spring constant is 112N/m, and b = 0.117kg/s. How long does it take for the amplitude to drop to half its initial value? (A*e-b*t/(2m))...

Hey, I've been trying to solve this question from Goldstein's Classical Mechanics. The picture I have of the question is from a later edition and the hint was removed from the question, the hint was let η3=ζ3...

Today I came across this design(as I am studying for my exams :P) And looking through my good Malvino, I found it. And I my mind was simply blown out by the concept of this oscillator. (If I got it right) http://pokit.org/get/957089cb8862c381d597a745b02c2763.jpg Malvino went here and there...

I have an interesting problem I have come across in my research. It results in the differential equation as follows: x''+2γ(x')^\nu+\omega_{o}^2x=g(t) Primes indicate the derivative with respect to t. \gamma and \omega are constants. The non-linearity comes from the first derivative x'...

Homework Statement A particle is in a region with the potential V(x) = κ(x2-l2)2 What is the approximate ground state energy approximation for small oscillations about the location of the potential's stable equilibrium? Homework Equations ground state harmonic oscillator ~ AeC*x2...

Homework Statement Consider an harmonic oscillator with time-dependent frequency as: \omega (t)=\omega_0 * \exp^{- \lambda t} Find the time dependence of the ground state energy of this oscillator for \lambda << 1 situation. Homework Equations H=H_{0} + V(t) H_{0} = \frac{p^2}{2m} +...

Hello, I am hoping someone can give me some advice. I am playing about with the design of a ring oscillator in an electronics simulations package. The ring has 5 inverters. As part of the assignment we were asked to ad in an extra inverter to the output of the ring and see if there was a...

Homework Statement Undamped oscillator's period T_0 = 12s. Damped oscillator's angular frequency \omega_1 = \omega_0 * 97\% where \omega_0 is the angular frequency of the undamped oscillator's. What is the ratio of consecutive maximum amplitudes? Homework Equations Equation of damped...

Homework Statement A 800g oscillator has a speed of 120.0 cm/s when its displacement is 1.5 cm and 55.0 cm/s when its displacement is 8.0 cm. a. What is the oscillator’s maximum speed? b. What is the oscillator’s maximum amplitude? Homework Equations A= sqroot(X^2+(V^2/w^2)...

Hello fellow computer physics nerds, I'm trying to write a program to plot the positions of the three particles connected by two springs (one dimensional) in Fortran 90. I have a main program block and a module that calls a PGPLOT. My problem is that the positions of the second and third...