Oscillator Definition and 1000 Threads

So, my book claims that the effective spring stiffness of an atom (according to the Einstein model) is 2ks,i, but in an example problem they state one quantum of energy for an oscillator with an interatomic spring stiffness of 5N/m with 5 quanta is \hbar \times \sqrt(\frac{4(5)}{\mathrm{weight...

Hi! I aim to use a piezoelectric wafer and get it to work as a loudspeaker by supplying it with a fluctuating voltage withing the audible region. I know this can be done using a simple DC to AC invertor/oscillator circuit, but the challenge is to build it as small as possible. I looked up...

Hi All, If there is something fundamentally wrong in my understanding of quantum mechanics, pardon me for I have just started learning it. We know that if we can come up with a solution for Schrodinger Equation of a Harmonic Oscillator, then we can generate further solutions by acting on it...

the damped oscillator equation: (m)y''(t) + (v)y'(t) +(k)y(t)=0 Show that the energy of the system given by E=(1/2)mx'² + (1/2)kx² satisfies: dE/dt = -mvx' i have gone through this several time simply differentiating the expression for E wrt and i end up with dE/dt =...

the damped oscillator equation: (m)y''(t) + (v)y'(t) +(k)y(t)=0 Show that the energy of the system given by E=(1/2)mx'² + (1/2)kx² satisfies: dE/dt = -mvx' i have gone through this several time simply differentiating the expression for E wrt and i end up with dE/dt =...

Given the Oscillator equation: \frac{d2s}{dt2} + \omega2s = 0 Show that the energy: E=1/2(\frac{ds}{dt})2 + 1/2\omega2s2 is conserved. Any help at all appreciated! Thankyou

I've been looking around and trying to figure it out, but I can't seem to figure out how the cosine function get's into the solution to the HO equation d2x/dt2=-kx/m. I know this is extremely basic, but could someone indulge me?

A particle has its wave function as the ground state of the harmonic oscillator. Suddenly the spring constant doubles (so the angular frequence dobules). Find the propability that the particle is afterwards in the new ground state. I did solve this, it was quite easy. But doing so I encountered...

Hi.Who can explain to me oscillator strength?

Ok, I know this question will sound really stupid but I'm just not following the derivation for the formula of degeneracy's given by 1/2(n+1)(n+2) This is what I get n1+n2+n3=n so for a given n1, n2+n3=n-n1 Then this is the line I don't understand (and I'm sure its something simple I'm...

Homework Statement At time t < 0 there is an infinite potential for x<0 and for x>0 the potential is 1/2m*w^2*x^2 (harmonic oscillator potential. Then at time t = 0 the potential is 1/2*m*w^2*x^2 for all x. The particle is in the ground state. Assume t = 0+ = 0- a) what is the probability that...

1. What is the angular frequency of a damped oscillator whose spring stiffness is 15 cm with a 19.6 N mass and a damping constant of 15 kg/s? 2. ω0 = √(k/m) ----where k = spring constant and m=mass ζ= c/(2√(mk)) -----where m = mass, k = spring constant, and c = damping constant...

Homework Statement Okay, so I know that I have to find the gain of the negative feedback part (1+ R2/R1). But then to find the transfer function of the bottom part of the oscillator, would the resistor and capacitor that are attached to the '+' terminal of the op amp be considered in...

Hello All, I would like a schematic that would help me to create a simple oscillator that can drive an aircore coil or other components at 3 to 7 MHz and 219 MHz approximately.Any help is appreciated. Gary

So, this has been bothering me for a while. Lets say we have the wavefunction of a harmonic oscillator as a general superposition of energy eigenstates: \Psi = \sum c_{n} \psi _{n} exp(i(E_{n}-E_{m})t/h) Is it true in this case that <V> =(1/2) <E> . I tried calculating this but i...

Quartz crystals are used in clocks to regulate time measurement. Does a quartz crystal convert heat energy to AC electrical energy? Duordi

Homework Statement Use the following trial function: \Psi=e^{-(\alpha)r} to estimate the ground state energy of the central potential: V(r)=(\frac{1}{2})m(\omega^{2})r^{2} The Attempt at a Solution Normalizing the trial wave function (separating the radial and spherical part)...

Hey guys, I'm designing a wireless cell phone charger that can be used inside a car for the senior design project. I'm feeding 12V DC into a colpitts oscillator which is fed into a B class power amplifier which will then be fed into the transmitting coil. Each one works great independently...

Homework Statement I need to find the momentum space wavefuntion Phi(p,t) for a particle in the first excited state of the harmonic oscillator using a raising operator. Homework Equations Phi_1(p,t)= "raising operator" * Phi_0 (p,t)The Attempt at a Solution In position space, psi_1 (x) =...

When people talk about harmonic oscillators it seems to me that they always assume either that the relationship of force and displacement is linear, or that it behaves in some sinusoidal fashion. Do you always have to assume one to be able to arrive at the other? Or is there something I'm...

Hi! The damped oscillator equation is as follows: x(t)= A exp(γt/2) cos(ωt) where ω= √( (w0)^2 + (γ^2)/4 ) I have attached a graph of a damped oscillator. The question is if I use graph to measure angular frequency, will it be w0 or ω? It should be w0 because if I put γ=0, I should...

Find under what conditions the transformation from (x,p) to (Q,P) is canonical when the transformation equations are: Q = ap/x , P=bx2 And apply the transformation to the harmonic oscillator. I did the first part and found a = -1/2b I am unsure about the next part tho: We have the...

Homework Statement A 3D harmonic oscillator has the following potential: V(x,y,z) = \frac{1}{2}m( \varpi_{x}^2x^2 + \varpi_{y}^2y^2 + \varpi_{z}^2z^2) Find the energy eigenstates and energy eigenvalues for this system. The Attempt at a Solution I found the energy eigenvalue to...

Homework Statement Find the energy eigenvalue. Homework Equations H = (p^2)/2m + 1/2m(w^2)(x^2) + λ(x^2) Hψ=Eψ The Attempt at a Solution So this is what I got so far: ((-h/2m)(∂^2/∂x^2)+(m(w^2)/2 - λ)(x^2))ψ=Eψ I'm not sure if I should solve this using a differential...

Homework Statement (See attachment) Homework Equations x = \sqrt{\frac{\hbar}{2m \omega}} ( a + a^{\dagger} ) x = i \sqrt{\frac{\hbar m \omega}{2}} ( a^{\dagger} - a ) The Attempt at a Solution In part a) I was able to construct a separable Hamiltonian for the harmonic...

Homework Statement Consider an underdamped harmonic oscillator (Q > 1/2) with a sinusoidal driving force Focos(ωdt). (a) (5 pts) By using differential calculus find ωd that maximizes the displacement amplitude. (b) (7 pts) By using differential calculus find ωd that maximizes the velocity...

Homework Statement An overdamped oscillator with natural frequency w and damping coefficient y starts out at a position xo>0. What is the maximum initial speed (directed toward the origin) it can have and not cross the origin? Homework Equations Overdamped Case Equation...

Homework Statement The motion of a linear oscillator may be represented by means of a graph in which x is abscissa and dx/dt as ordinate. The histroy of the oscillator is then a curve a)show that for an undamped oscillator this curve is an ellipse b) show (at least qualitatively) that if a...

Ground State Wave Equation: ψ0=(a/∏)(1/4)e(-ax2/2) Prove the Heisenberg Uncertainty principle ≥h(bar)/2 by way of expectation values. First I found <x>=0 because it was an odd function then I found <Px>=0 because it was an odd function Then <x2>=∫(a/∏)(1/2)x2e(-ax2)/2dx=1/2a by way of...

Hi, So, I have a doubt regarding the equations for vertical oscillations on a spring. My book says the net force on the block is: F = k(d+y) - mg. If we define d the distance at -kd = mg. I, don't understand, the reason being: When the block is moving downwards, if its performing...

I believe this is pretty standard. Given a mass m on a spring with spring constant k, a solution to the second order differential equation of motion m\ddot{x} = -kx, is x = cos ωot, and ωo = \sqrt{k/m}. If that same oscillator is driven with a force F(t) = Fo cos ωt the equation of motion...

Homework Statement A simple harmonic oscillator has an amplitude of 0.1 m. At what displacement will its kinetic and potential energies be equal? Homework Equations The Attempt at a Solution I'm trying to figure out how to solve this problem but I'm totally stuck and even don't...

Homework Statement An overdamped oscillator with natural frequency w and damping coefficient g starts out at postion x0 > 0. What is the maximum initial speed towards the origin it can have without crossing the origin? Homework Equations x(t) for overdamped oscillator The Attempt at...

Homework Statement The problem wants me to calculate (Δx)^2 and (Δp)^2 to find the uncertainty principle. Delta x is the variance and the problem gives the formula as.. Δx= <n|x^{2}|n>-<n|x|n>^{2}Homework Equations x=\sqrt{\frac{\hbar}{2m \omega}}(A^{-}+A^{+}) Where A+ and A- are the raising...

This is a problem I've been trying to solve for quite some time now. Any help would be appreciated. Homework Statement When a person with the mass of 105kg sits in a car, the body of the car descends by 2,5cm in total. In the car there are four shock absorbers filled with oil and a spring...

Homework Statement I was asked an interesting question once that I'd like to solve but have no idea where to start. It's hard to remember the exact details but basically: Two electrons are in a harmonic oscillator potential but in two separate states \left | m \right \rangle and...

Homework Statement The displacement amplitude of a lightly damped oscillator with m=0.250kg and k=6400N/m is observed to decrease by 15% in exactly five minutes a) Calculate the fraction (in%0 of the initial mechanical energy of the oscillator that has been converted to other forms of energy...

Homework Statement A harmonic oscillator has angular frequency ω and amplitude A. What is the magnitude of the displacement when the elastic potential energy is equal to the kinetic energy? (Assume that U = 0 at equilibrium.) Express your answer in terms of the variables ω and A...

hello, new here and confused about Newton second Law. given: vertical mass damper system, position of the mass: x(t)=sin(t) velocity is: v(t)=cos(t) acceleration is: a(t)=-sin(t) function x(t): above x-axis describes position of the mass below the vertical equilibrium point, which (below) is...

I need to find the value σ for which: ψ0(x) = (2πσ)-1/4 exp(-x2/4σ) is a solution for the Schrodinger equation I know the equation for the QHO is: Eψ = (P2/2m)ψ + 1/2*mw2x2ψ I've tried normalizing the wavefunction but I end up with a σ/σ term :( Any help would be greatly...

How does one go about plotting the effects of the frequency of the driving force vs the amplitude of the masses in a system such as the one pictured below? Assume that I have already figured out what my two angular frequencies are, and the amplitues under driven force (the actually equations...

I need to create a 10 MHz square wave clock signal which gets terminated into a 50 ohm resistor for use by a waveform generator. The specifications for the waveform generator suggest a 12 to 14 dBm power level for the input clock. ie. a power level of ~16-25mW. So I've been looking to...

Over which interval do the wave functions of a harmonic oscillator form a complete and orthogonal system? Is it (-inf,+inf)? The case with particle in a box is rather clear(system is complete and orthogonal only for the interval of the well), however the harmonic oscillator is a bit less intuitive.

here is a link to the pdf file with my question and answershttp://dl.dropbox.com/u/2399196/harmonic%20osc.pdf i'm not sure where to start, because i don't want to assume anything that i haven't been given. i'm stuck on part (iv) where i have to derive explicit expressions for 2 wave functions...

I've heard before that it's because when you expand around a minimum point in the potential energy you get a quadratic function, but I can't recall where I read this. Can anyone point me in the right direction, or give their own explanation? I only ask because I just solved a problem in my...

I'm new to electronics and I just bought an electronics project kit and built a pulse tone oscillator (the schematic is attached). The manual doesn't go into very much detail about how the circuit works. I've built a few simple circuits before in physics 2 and I understand how the individual...

Homework Statement This is a relxation oscillator that's realized by UJT. The graph is included. What is the output of the circuit? http://img821.imageshack.us/img821/2274/ujtok.jpg Homework Equations http://www.allaboutcircuits.com/vol_3/chpt_7/8.html The Attempt...

Just have a few questions regarding the method of solving the damped-driven harmonic oscillator. Once we have rewritten the differential equation in terms of z and it's derivatives, we try a solution z(t) = Ce^{i \omega t}. When we sub in z and it's derivatives we then rewrite the complex...

Hey guys, I'm working on a voltage controlled oscillator to use in a modular synth system and here's the schematic. http://ecelab.com/circuit-vco-555.jpg I also have a one octave keyboard that I made and each key is 1/12 of a volt. My question is to what frequency I should tune the oscillator...

Homework Statement The position of the center of the box shown is given by the equation x = 4.4 m * cos(29/sec * t) -How long does it take the box to move from -2.2 m to +2.2 m? Homework Equations x = 4.4 m * cos(29/sec * t) The Attempt at a Solution ±.5=cos29t [arccos(-.5) -...