Oscillator Definition and 1000 Threads

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...

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) -...

Homework Statement A physical system is designed having the following equation of motion md2x/dt2 + c(dx/dt) - kx = 0. (a) From the corresponding subsidiary equation, find the solution to this equation of motion. (HINT: use the solution of the damped harmonic oscillator as a guide)...

I was reading through a book on statistical physics when i came across this sentence: "An Einstein solid has two degrees of freedom for every oscillator." How is this possible? I picture an oscillator (ex. mass on spring) to move only in one dimension, thus one degree of freedom. Where does...

the problem is attached as an image. im having troubles with the question. I'm assuming this is an induction question? i can prove it for the basis step n=0. but I am having trouble as to what i have to do for n+1 (inductive step). any help or hints would be great!thanks

What are 2 applications of an oscillator circuit, I need help with this!? I can only find one... :frown: thanks for any help

Homework Statement This problem was already answered: "I have to find the allowed energies of this potential: V(x)= (mω2^2)/2 for x>0 infinite for x<0 My suggestion is that all the odd-numbered energies (n = 1, 3, 5...) in the ordinary harmonic osc. potential are...

http://img689.imageshack.us/img689/7084/ujte.jpg This is a Relaxation Oscillator circuit with UJT. I need to A) Explain what is UJT, explain its relation ratio of η for the UJT, and explain what Vp is. And in B) Explain how does the circuit work, and what is the output (or turnout) of the...

Hello I am trying to understand how exactly an oscillator circuit work and how to build one. So I was palying around in falstad and made this: the following is link. tried to get around spam filter so.. write without spaces h t t p s : / / w w w . f a l s t a d . c o m / c i r c u i t /...

Local oscillators that is used in RF transmitters for AM modulation.Any help is appreciated. Thanks !

Homework Statement Consider a quantum mechanical particle moving in a potential V(x) = 1/2mω2x2. When this particle is in the state of lowest energy, A: it has zero energy B: is located at x = 0 C: has a vanishing wavefunction D: none of the above Homework Equations The...

Homework Statement A mass of 0.3kg hangs motionless from a vertical spring whose length is 0.8m and unstreteched length is 0.65m. The mass is then pulled down so the spring has the length of 0.9m and given an initial speed upwards of 1.2m/s upwards. What is the maximum length of the...

Homework Statement I need to transform the Hamiltonian of a coupled Harmonic Oscillator into the sum of two decoupled Hamiltonians (non-interacting oscillators). Homework Equations H = H1 + H2 + qxy, where H1=0.5*m*omega^2*x^2+0.5m^-1P_x^2 and H2=0.5*m*omega^2*y^2+0.5m^-1P_y^2, and q is...

Homework Statement Use a series expansion ψ=A0x0+A1x1+A2x2+... to determine the three lowest-order wave functions for a harmonic oscillator with spring constant k and mass m, and show that the engergies are the expected values. Homework Equations Series expansion given above Time...

(NOTE, this is not a homework problem, but it sure seems like one) Hello, I am mounting a component onto structure and I need to determine the maximum force input into the component. My system can be represented by a base driven two degree of freedom oscillator...

Hello, I am mounting a component onto structure and I need to determine the maximum force input into the component. My system can be represented by a base driven two degree of freedom oscillator: http://www.freeimagehosting.net/newuploads/xowmr.png I need to determine the force...

Hello everyone, i'm looking for anypaper or such kind of thing that explain the resolution of the harmonic oscillator in the Dirac Theory. I have worked with the exact spin symmetry. I feel like a fish out the water and I'm sure that there are lot of bibliography about this area, but i...

i have a wien bridge oscillator by using ±15V power supply. its output is sine wave. but i have a question. is the output become ac or still dc while it is oscillate with 10kHz?