Harmonic oscillator Definition and 743 Threads

  1. 2

    Diffe Q, a forced harmonic oscillator

    okay this is kind of a quick one when youre solving a forced harmonic oscillator for an initial condition by the method of undetermined coefficients, you do the part for the homogenoues equation first and come up with somethign like ke^at + ce^bt. Now when you goto solve for those constants k...
  2. F

    Solve for Displacement in Harmonic Oscillator

    Can someone check my work please I'm pretty sure I don't have the right answer but I can't figure out what I have wrong. The question is: A simple harmonic oscillator has total energy E=1/2kA^2 where A is the amplitude of oscillation. For what value of the displacement does the kinetic...
  3. K

    Adding a small extra potential to a simple harmonic oscillator

    Hi, I've been scouring through many textbooks to try find some kind of solution to a question I have been asked for a problem sheet and was wondering if any1 would be able to help. The question is as follows; The simple harmonic oscillator with hamiltonian H = (p^2/2m) + (1/2(mw^2x^2) is...
  4. L

    Harmonic Oscillator kinetic and potential energies

    A simple harmonic oscillator has a total energy of E. (a) Determine the kinetic and potential energies when the displacement is three-fourths the amplitude. (Give your answer in terms of total energy E of the oscillator.) Kinetic energy ______________ x E <----(times E) Potential energy...
  5. E

    Calculating Probability for Harmonic Oscillator States

    I have the U(x) functions for the ground state and first excited state of the simple harmonic oscillator. I also have the psi (x,0) wave function for this situation. How do I find the probability the particle is in a particular state? Is it simply the integral of psi(x,0) * u(x) dx evaluated...
  6. P

    How Does a Shifted Harmonic Oscillator Decompose into Eigenfunctions?

    I have a wave function which is the ground state of a harmonic oscillator (potential centered at x=0)... but shifted by a constant along the position axis (ie. (x-b) instead of x in the exponential). How does this decompose into eigenfunctions?? I know it's an infinite sum... but I can't...
  7. S

    Analytical mechanics: 2D isotropic harmonic oscillator

    I'm stuck on this problem: The initial conditions for a two-dimensional isotropic oscillator are as follows: t=0, x=A, y=4A, v=0i +3wAj (vector) where w is the angular frequency. Find x and y as functions of t. Where do I even begin with this problem. I take it A = constant. Can anyone...
  8. Reshma

    Coupled Harmonic oscillator problem

    I need your help to solve this problem on coupled harmonic oscillators. Two masses m1 and m2 are attached to two rigid supports by means of springs of force constants k1 and k2 respectively. The masses are connected to a third spring of force constant k3. The masses are free to move along the...
  9. A

    Harmonic Oscillator: Energy Levels Explained

    why is the energy levels of the harmonic oscillator En=(N+1/2)hf?
  10. B

    Damped harmonic oscillator physics

    Please I don't understand this problem at all: Consider a driven damped harmonic oscillator.Calculate the power dissipated by the damping force? calculate the average power loss, using the fact that the average of (sin(wt+phi) )^2 over a cycle is one half? Please can I have some help for...
  11. A

    Harmonic Oscillator: Lowest Allowed Energy Not E=0?

    why is the lowest allowed energy not E=0 but some definite minimum E=E0?
  12. B

    Why Does Only V(10) Contribute in Perturbed Harmonic Oscillator Calculations?

    I've been given a question which asks to calculate the probability of finding an electron is an excited state for a Harmonic oscillator perturbed by an electric field pulse E(t) as t tends to infinity. E= -exA\exp{(\frac{-t}{\tau})} I knew I had to use the Time dependent perturbation...
  13. S

    Solving Harmonic Oscillator Coefficients w/ Hermite Polynomials

    Ok, fairly basic quantum mechanics assignment. One question deals with (I think) the coefficients of the Hermite polynomial. Unfortunately, the lecturer hasn't told us anything about this method, so I donn't know what it's called or what the point of it is, and it's not in any of the examples...
  14. E

    Driven, damped harmonic oscillator - with particular solution

    Driven, damped harmonic oscillator -- need help with particular solution Consider a damped oscillator with Beta = w/4 driven by F=A1cos(wt)+A2cos(3wt). Find x(t). I know that x(t) is the solution to the system with the above drive force. I know that if an external driving force applied...
  15. M

    Zero-point energy of a linear harmonic oscillator

    Hi. I'm given a problem with a harmonic oscillator where the potential is V= (kx^2)/2 with a mass m (KE = 1/2 mv^2). I have to use the Heisenberg Uncertainty principle to show what the minimum energy is, but I'm not sure where to start... I think I have to combine KE + V and minimize that, but...
  16. B

    How Does Friction Affect the Amplitude of a Harmonic Oscillator Over Time?

    Please help 1) The mechanism which powers the clock (using a harmonic oscillator to keep time with friction) Since the clock has friction the oscillation amplitude decreases in time. If the oscillation amp is unity at t=0 what will the amp be after 10 sec? I believe we need to use the...
  17. R

    Quantum harmonic oscillator system

    Hi, I am wondering how i would go about calculating the canonical partition function for a system of N quantum harmonic oscillators. The idea of the question is that we are treating photons as oscillators with a discrete energy spectrum. I'm confused as whether to use Maxwell-Boltmann...
  18. M

    Harmonic Oscillator: Position Expectation Value & Ground State

    why is the expectation value of the position of a harmonic oscillator in its ground state zero? and what does it mean that it is in ground state? is ground state equal to n=0 or n=1?
  19. C

    Exploring the Eigenfunctions and Eigenvalues of a 2D Harmonic Oscillator

    This might be another problem that our class hasn't covered material to answer yet - but I want to be sure. The question is the following: Find the eigenfunctions and eigenvalues of a two-dimensional isotropic harmonic oscillator. Again, I need help simply starting.
  20. E

    Lightly Damped Harmonic Oscillator

    Question: (a) Show that the total mechanical energy of a lightly damped harmonic oscillator is E = E_0 e^{-bt/m} where E_0 is the total mechanical energy at t = 0. (b) Show that the fractional energy lost per period is \frac{\Delta E}{E} = \frac{2 \pi b}{m \omega_0} = \frac{2...
  21. B

    Expectation value, harmonic oscillator

    Hi, I have to find the expectation values of xp and px for nth energy eigenstate in the 1-d harmonic oscillator. If I know <xp> I can immediately find <px>since [x,p]=ih. I use the ladder operators a_{\pm}=\tfrac1{\sqrt{2\hslash m\omega}}(\mp ip+m\omega x) to find <xp>, but I get a complex...
  22. C

    Initial Conditions of an Undamped Forced Harmonic Oscillator

    The equation of motion of an undamped harmonic oscillator with driving force F=F_ocos(\omega*t) is x(t) = Acos(\omega_0*t) + Bsin(\omega_0*t) + \frac{F_0}{m}\frac{cos(\omega*t)}{\omega_0^2-\omega^2} I am to determine the initial conditions such that the undamped oscillator begins steady...
  23. W

    Solving a Simple Harmonic Oscillator Problem

    For some reason this problem has me stuck. It isn't homework, but it might be on the exam Tommorrow. If anyone is still awake, please steer me in the right direction. Thank you A simple harmonic oscillator has a total energy of E. (a) determine the kinetic and potential energies when...
  24. maverick280857

    Where Can I Find Classical Treatments of the Two Body Harmonic Oscillator?

    Hi friends I would be grateful if someone could point me to a mathematical treatise (on the internet) about the two body simple harmonic oscillator (classical mechanics only, but no Lagrangian/Hamiltonian...just energy, momentum, Newton's Laws). I am googling right now but all I find is...
  25. E

    Damped Harmonic Oscillator & Mechanical Energy

    Question: A damped harmonic oscillator loses 5.0 percent of its mechanical energy per cycle. (a) By what percentage does its frequency differ from the natural frequency \omega_0 = \sqrt{k/m}? (b) After how may periods will the amplitude have decreased to 1/e of its original value? So, for...
  26. Y

    Why Does a Half Harmonic Oscillator Only Allow Odd Quantum Numbers?

    Why does the half of a harmonic oscillator potential allow only odd values of n? Thx
  27. W

    How to Solve a Damped Harmonic Oscillator Problem?

    Hi, I'm having a lot of trouble with a damped harmonic oscillator problem: A damped harmonic oscillator consists of a block (m=2.00kg), a spring (k=10 N/m), and a damping force (F=-bv). Initially it oscillates with an amplitude of 25.0cm. Because of the damping force, the amplitude falls...
  28. G

    Damped Simple Harmonic oscillator

    a damped simple harmonic oscillator has mass m = 260 g, k = 95 N/m, and b = 75 g/s. Assume all other components have negligible mass. What is the ratio of the amplitude of the damped oscillations to the initial amplitude at the end of 20 cycles (Adamped / Ainitial)? having trouble getting...
  29. M

    Solving an Isotropic Harmonic Oscillator with Four Identical Springs

    hi, I was going through my homework and i came to a problem that i can't seem to get. Consider the mass attached to four identical spring. Each spring has the force constant k and unstreched length L_0, and the length of each spring when the mass is at the origin is a(not necessarily the same...
  30. R

    Help with QM harmonic Oscillator Question

    Ok so i have been instructed to normalize N*x*exp(-ax^2), so i squared the function and trying to take the integral. I am a) assuming that the integration should run from the negative value of the amplitude or -A to the positive value of the Amplitude of A, i have a formula for A. My assumption...
  31. E

    The one-dimensional harmonic oscillator

    Dealing with the one-dimensional harmonic oscillator I'm trying to find a general formula for \int_{-\infty}^{\infty} \xi^p H_n(\xi) H_k(\xi) d\xi there H_n(\xi) and H_k(\xi) are hermite polynomials and p is an integer ( p\geq 0). I can found the answer for p=0 and p=1 but I can't find...
  32. Y

    Average total energy of 3D harmonic oscillator in thermal equilibrium

    Hi, From knowing that the 3D harmonic oscillator has 3 degrees of freedom, how do you conclude that the average total energy of the oscillator has energy 3kT? Thanks, Ying
  33. C

    Damped Harmonic Oscillator Approximation?

    For a simple damped oscillator... \text {Apparently if } \beta \ll \omega_0 } \text { then ...} \omega_d \approx \omega_0[1-\frac {1}{2}(\beta/\omega_0)^2]} Given that: \beta=R_m/2m \text { (where } R_m= \text {mechanical resistance) } \text { and } \omega _d=\sqrt{(\omega...
  34. E

    How Does Damping Affect the Frequency and Amplitude of a Harmonic Oscillator?

    Question: A damped harmonic oscillar loses 5.0 percent of its mechanical energy per cycle. (a) By what percentage does its frequency differ from the natural frequency \omega_0 = \sqrt{k/m}? (b) After how many periods will the amplitude have decreased to 1/e of its original value? (a) Let E(t)...
  35. quasar987

    Simple harmonic oscillator general solution

    In my mechanics textbook is given an exemple of how to find the general solution of the of the equation of motion for a force -kx (the simple harmonic oscillator problem). He begin his analysis and finds that e^(iwt) and e^(-iwt) are both solutions. Hence C1*e^(iwt) and C2*e^(-iwt) are also...
  36. K

    Can Dark Energy Undergo Simple Harmonic Oscillation?

    If the universe oscillates between a Big Bang and a Big crunch, can two small volumes of dark energy, at opposite ends of it, be considered to be undergoing simple harmonic oscillation? The potential energy of an oscillator could be given by G m1 m2 /r where m1 is the mass of a volume of...
  37. K

    Universe as a simple harmonic oscillator

    If the universe is a simple harmonic oscillator then it must be symmetrical and divided into two halves , each half with approximately 10^52 kg of mass at its centre of mass. If the universe reaches about 10^26 metres in about 10^18.5 seconds then using E = ( n + 1/2)h w for an oscillator we...
  38. K

    Oscillating universe and harmonic oscillator

    If the universe oscillates between a Big Bang and a Big crunch, can two particles at opposite ends of it, be considered to be undergoing simple harmonic oscillation? If the potential energy of the oscillator is given by G m1 m2 /r and m1 is the mass of the universe,10^52 kg,r = 10^26 metres...
  39. H

    Raising Operator (Harmonic Oscillator)

    This is (another!) question I cannot solve The ground state wavefunction for the harmonic oscillator can be written as $\chi _0 = \left( {\frac{\alpha } {\pi }} \right)^{\frac{1} {4}} \exp \left( {\frac{{ - \alpha x^2 }} {2}} \right)$ where $\alpha = \sqrt {\frac{{mk}} {{\hbar ^2...
  40. J

    Solving motion of undamped harmonic oscillator

    The question is: Solve for the motion of the undamped harmonic oscillator with an applied force F, treated in class, when the force is no longer constant but has the form F=F0+kT, where Fo and k are constants. Use the intial conditions x(0)=d and x'(0) =v0. I'm trying to solve this problem...
  41. S

    Webpage title: How to Calculate <x> for a One-Dimensional Harmonic Oscillator

    Here's the problem: A one dimensional harmonic oscillator has mass m and frequency w. A time dependent state psi(t) is given at t=0 by: psi(0)=1/sqrt(2s)*sum(n=N-s,n=N+s) In> where In> are the number eigenstates and N>>s>>1. Calculate <x>. Show it varies sinusoidally; find the...
  42. C

    Formula for the harmonic oscillator is f"(x)+W^2 * X(t)=0

    can anyboy show to me why the formula for the harmonic oscillator is f"(x)+W^2 * X(t)=0. Please I spent a whole afternoon trying to figure it out and I just wasted my time. Thanks
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