Oscillator Definition and 1000 Threads

I have trouble understanding how damping affects the period (of a torsion pendulum). I know that damping affects the amplitude of the oscillator, however how would damping change the period then? I have a feeling this has to do with angular frequency, w, given by: w = sqrt( (k/m) -...

Homework Statement Given a particle is confined in a one dimensional harmonic oscillator potential, find the matrix representation of the momentum operator in the basis of the eigenvectors of the Hamiltonian. Homework Equations Potential: V(x) = 0.5 m w^2 x^2 where m is the mass of...

I am looking into the calculations of a harmonic oscillator potential for nuclei single-particles. The information I am looking at is at: http://en.wikipedia.org/wiki/Shell_model the specific section “Deformed harmonic oscillator approximated model” The specific question is, I don’t...

Homework Statement The assignment is to create a square wave oscillator using an op-amp in Multisim. The wave's frequency should be 1 kHz and the duty cycle 60%. Homework Equations f = 1 / (R*C) R1 < R R1 < Rf I guess. The Attempt at a Solution Here's what I've done...

Homework Statement I've been pondering the analogy between an RLC circuit and a damped harmonic oscillator. The inductor serves the role of the inertia, leading a finite charging frequency. What happens if we remove the inductor, so that the system consists just of a charged capacitor...

Homework Statement A particle moves along x-axis subject to a force toward the origin proportional to -kx. Find kinetic (K) and potential (P) energy as functions of time t, and show that total energy is contant. Homework Equations K = (1/2)m*v^2 P = (1/2)k*x^2 E = K+P x = Asin(wt...

Does anyone know why a harmonic potential gives rise to coherent states? In other words, what is special about a quadratic potential that causes the shifted ground state to oscillate like a classical particle without dispersing so as to saturate the uncertainty principle? Any help or insight...

Homework Statement A simple harmonic oscillator consists of a block of mass 2.30 kg attached to a spring of spring constant 440 N/m. When t = 1.70 s, the position and velocity of the block are x = 0.135 m and v = 3.130 m/s. (a) What is the amplitude of the oscillations? What were the (b)...

Homework Statement A particle is inside of a potential described by: H = p^2/2m + 1/2kx^2, x between -L/2 and L/2 H = infinity, otherwise. my task is to compute a first-order approximation to the energies of this potential. The Attempt at a Solution I attempted to use...

Homework Statement I have read the chapter twice and I have read through the notes several times to help me with the homework assignment. It deals with damped Harmonic Oscillations. Problem: You have a mass submerged horizontally in oil and a spring with a k of 85 N/m pulls on a mass of...

Homework Statement A damped harmonic oscillator originally at rest and in its equilibrium position is subject to a periodic driving force over one period by F(t)=-\tau^2+4t^2 for -\tau/2<t<\tau/2 where \tau =n\pi/\omega a.) Obtain the Fourier expansion of the function in the integral...

Hi, does anyone know of a good resource that focuses on the history of the harmonic oscillator and other classical systems like the vibrating string and vibrating drum? I need to talk about the historical aspect in a project and was having a hard time finding some good material. anyway let me...

Homework Statement An un-damped driven harmonic oscillator satisfies the equation of motion: ma+kx=F(t) where we may write the un-damped angular frequency w-naught^2=k/m. The driving force F(t)=F-naught*sin(wt) is switched on at t=0. Find x(t) for t>0 for initial conditions x=0, v=0,at t=0...

Homework Statement The general solution of the underdamped oscillator is given by x(t) = exp(-Bt)*[(A1)cos{(w1)t} + (A2)sin{(w1)t}] Solve for x0 = x(t=0) and v0 = v(t=0) in terms of A1 and A2. Then solve for A1 and A2 in terms of x0, v0 , and w1. Homework Equations w1 = sqrt{ (w0)^2 - B^2...

Homework Statement A car is moving along a hill at constant speed on an undulating road with profile h(x) where h'(x) is small. The car is represented by a chassis which keeps contact with the road , connected to an upper mass m by a spring and a damper. At time t, the upper mas has...

See post two.

Homework Statement A driven oscillator satisfies the equation x'' + omega2=F0cos(omega(1+episilon)t] where episilon is a positive constant. Show that the solution that satisfies the iniitial conditions x=0 and x'=0 when t=0 is x= (F0*sin(.5episilon*omega * t)...

Hi, I originally posted this question in the homework section, but I really don't need any help calculating anything, my answers are right. I'm having conceptual trouble, so I figured that this question belongs here. So, let's say there is a field driving a single atomic oscillator (hydrogen...

Homework Statement A damped oscillator satisfies the equation x'' + 2Kx' + \Omega^2 *(x) where K and \Omega are positive constants with K < \Omega (underdamping). i)At time t =0 the particle is released from rest at the point x=a . Show that the subsequent motion is given by...

I have been given at t=1.00 a position and velocity. And the spring constant and mass. I have found the maximum amplitude. The question is, where was the block at time t=0? And apparently this can be done without solving for the phase constant and making an equation. The question doesn't...

Hi all, I have to determine the potential energy of a hanging spring with a mass m in the end and spring constant k. I try to write down the force in the system F = m*g + k*x and integrate the force in order to get the potential energy E_p = m*g*x+0.5*k*x*x Does this look correct...

Homework Statement Predict the wavenumber (cm-1) position of infrared absorption due to fundamental vibration from v=0 to v=1 and 2nd overtone from v=0 to v=3. For a harmonic occilator whose frequency=8.00x1013 s. Homework Equations Energy expression for harmonic oscilator: Ev=...

I am working with the following harmonic oscillator formula. \psi_n \left( y \right) = \left( \frac {\alpha}{{\pi}} \right) ^ \frac{1}{{4}} \frac{1}{{\sqrt{2^nn!}}}H_n\left(y\right)e^{\frac{-y^2}{{2}}} Where y = \sqrt{\alpha} x And \alpha = \frac{m\omega}{{\hbar}} I...

We have a potential that is (1/2)kx^2 for x>0 and is infinity for x<0 ( half harmonic oscillator. Now i want to calculate the bound states of the system for given E. My question is this: Do we apply 1. \int p(x) dx = (n - \frac{1}{4} ) h ( Since there is only one turning point that can...

The displacement of a harmonic oscillator is given by x = A Cos(wt + Phi) The phase angle phi is equally likely to have any value in the range 0 < Phi < 2Pi, so the probability W(Phi) that Phi lies between Phi and Phi + delta-Phi is delta-Phi/(2Pi). For a fixed time t, find the probability...

i got these question which i do not know how to do... Qn. In a forced mechanical oscillator, show that the following are frequency independent. i) the mechanical amplitude at low frequencies. ii) the velocity amplitude at velocity resonance. iii) the acceleration amplitude at high...

Homework Statement Hello. I am attempting to evaluate the classical action of a harmonic oscillator by using the Euler-Lagrange equations. Homework Equations The Lagrangian for such an oscillator is $$ L=(1/2)m(\dot{x}^2-\omega^2 x^2) $$ This is easy enough to solve for. The classical action...

I wish to graph a couple of the waveforms of a harmonic oscillator. I have consulted several resources and have found two that I like but the final equation differs even though they are both labeled normalized harmonic oscillator wavefunction. The first reference explains how the harmonic...

1. At a certain time the wavefunction of a one-dimensional harmonic oscillator is \psi(x) = 3\phi0(x) + 4\phi1(x) where \phi0(x) and \phi1(x) are normalized energy eigenfunctions of the ground and first excited states respectively. Normalize the wavefunction and determine the probability...

if the quantum oscillator was used to describe a diatomic molecule, then at T=0, the molecule shouldn't be vibrating at all. but using the quantum oscillator model, the molecule still has a minimum energy at its ground state related to its zero point energy. does this mean a molecule at T=0 DOES...

Alright, I'm sure I'm missing something extremely simple, but in Griffiths (and another text I'm reading) coherent states are mentioned as eigenfunctions of the annihilation operator. I just don't understand: a) how you can have an eigenfunction of the annihilation operator (other than |0>) if...

I was looking at the Clapp oscillator located here: http://en.wikipedia.org/wiki/Clapp_oscillator Can someone please explain what the transistor is for? Also, since when the oscillator oscillates, the direction of the current flips...does this have any effect on the battery? Lastly, if you...

I'm reading Griffiths', and I had a question about the harmonic oscillator. Griffiths solves the Schrodinger equation using ladder operators, and he then says that there must be a "lowest rung," or \psi_{0}, such that a_\psi_{0} = 0. I'm guessing this also means that E = 0 for a_\psi_{0}...

Homework Statement A particle oscillates between the points x = 40mm and x = 160mm with an acceleration a = k(100-x) where k is a constant. The velocity of the particle is 18mm/s when x=100 and zero at x = 40mm and x = 160mm. Determine a) the value of hte constant k, b) the velocity when x =...

Problem Show that in the nth state of the harmonic oscillator \langle x^2 \rangle = (\Delta x)^2 \langle p^2 \rangle = (\Delta p)^2 Solution This seems too simple... I'm not sure if it's correct... It is obvious that \langle x \rangle = 0... this is true because the parity of the...

Problem A harmonic oscillator consists of a mass of 1 g on a spring. Its frequency is 1 Hz and the mass passes through the equilibrium position with a velocity of 10 cm/s. What is the order of magnitude of the quantum number associated with the energy of the system? Solution? Okay, so the...

http://img179.imageshack.us/img179/2245/springgraph226fe577uv1.jpg -------------------------------------------------------------------------------- A 3.9 kg block is attached to a horizontal spring and undergoes simple harmonic motion on a frictionless surface according to the graph shown...

Homework Statement A simple harmonic oscillator is displaced 5.00 cm from equilibrium and released at t=0s. Its position at t=1.5 s is 2.00 cm. What is the angular frequency of the oscillator? The book says the answer is 0.773. Homework Equations F= 1/T = w/ (2*pi) (theta,f) -...

Hello everyone. My question is quite long, so please bear with me; my professor is very busy and cannot help me at the moment, and I can't contact the course tutor. We have the DE \ddot \theta + \alpha \dot \theta + \sin{\theta } = \epsilon \cos{\omega t} where theta is the angle the...

Homework Statement An object of mass m and another of mass M = 2m are connected to 3 springs of spring constant horixontally. The displacement of the two masses are defined as x and y. When x = y = 0, the springs are unextended. a) Write down the two coupled equations of motion...

[SOLVED] Identical Particles in a 1-D Harmonic Oscillator Homework Statement Three particles are confined in a 1-D harmonic oscillator potential. Determine the energy and the degeneracy of the ground state for the following three cases. (a) The particles are identical bosons (say, spin 0)...

hi guys I am new in this forum hope I am not lost.I am desperately asking for your help on how a wein bridge oscillator works by reffering to phase shift and attenuation of the wein bridge networkthe phase shift and amplification provided by the amplifier and the type of feedback produced.thank you

The equation for motion for a damped oscillator is: x(double dot) + 2x(dot) + 2 = 0 a) Show that x(t)= (A + Bt)e^-t Where A and B are constants, satisfies the equation for motion given above. b) At time t = 0, the oscillator is released at distance Ao from equilibrium and with a...

Hi, I am looking for some plain english teaching of oscillators! I am particularly interested in the use of posotive feedback as I have just studied op-amp's and negative feedback and now want to understand oscillators. I have plenty of information from an old book but to be honest it is...

Hi everyone, Could someone please help me with this problem? Homework Statement A simple harmonic oscillator takes 11.5s to undergo four complete vibrations. a. Find the period of its motion b. Find the frequency in Hertz c. Find the angular frequency in radians per second...

Hi everyone. I have a project where I need to find a situation this is, or is similar to, a damped oscillator. That is, the Differential Equation (DE) for the system must follow: x'' + ax' + bx = 0 And, further, it must have some situation corresponding to being 'driven' or 'forced', that...

Homework Statement Consider the SHO inside a square well, which looks like a soda can cut in half inside of a box. \[ V(x,y) = \left\{ \begin{array}{l} \frac{1}{2}kx^2 ,{\rm{ }}y{\rm{ }} < {\rm{ }}|a| \\ \infty ,{\rm{ }}y{\rm{ }} \ge {\rm{ }}|a|{\rm{ }} \\ \end{array} \right\} \]...

[SOLVED] Simple Harmonic Oscillator Homework Statement The equation of motion of a simple harmonic oscillator is (second derivative of x wrt t) d2x/dt2 = -9x, where x is displacement and t is time. The period of oscillation is? Homework Equations 2 pi f = omega f = 1/T...

Homework Statement consider V(x,y) = inf, |y| > a; 1/2kx^2, |y|<=a. find the energies of this potential. my initial idea was to just look for solutions of the form X(x)*Y(y), and solve for the separation constant, which should give me the energy, right?

Hi there I found the following nice webpage that gives a brief discussion of the Lorentz Oscillator Model of the atom: http://webphysics.davidson.edu/Projects/AnAntonelli/node5.html. It's part of someone's honours thesis. (Unfortunately the pictures are very small, but nevermind.) Can...