Simple harmonic oscillator Definition and 114 Threads

In mechanics and physics, simple harmonic motion (sometimes abbreviated SHM) is a special type of periodic motion where the restoring force on the moving object is directly proportional to the object's displacement magnitude and acts towards the object's equilibrium position. It results in an oscillation which, if uninhibited by friction or any other dissipation of energy, continues indefinitely.
Simple harmonic motion can serve as a mathematical model for a variety of motions, but is typified by the oscillation of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's law. The motion is sinusoidal in time and demonstrates a single resonant frequency. Other phenomena can be modeled by simple harmonic motion, including the motion of a simple pendulum, although for it to be an accurate model, the net force on the object at the end of the pendulum must be proportional to the displacement (and even so, it is only a good approximation when the angle of the swing is small; see small-angle approximation). Simple harmonic motion can also be used to model molecular vibration as well.
Simple harmonic motion provides a basis for the characterization of more complicated periodic motion through the techniques of Fourier analysis.

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  1. C

    Simple Harmonic Oscillator - Hamiltonian

    See post two.
  2. A

    Finding Position of Simple Harmonic Oscillator

    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...
  3. M

    Deriving Potential Energy and Variance in a Simple Harmonic Oscillator

    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...
  4. N

    Simple Harmonic Oscillator Help

    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 =...
  5. K

    Simple Harmonic Oscillator and period

    [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...
  6. N

    Perturbation of the simple harmonic oscillator

    [SOLVED] Perturbation of the simple harmonic oscillator Homework Statement An additional term V0e-ax2 is added to the potential of the simple harmonic oscillator (V and a are constants, V is small, a>0). Calculate the first-order correction of the ground state. How does the correction change...
  7. E

    How Does an Electric Field Affect the Quantum Harmonic Oscillator?

    [SOLVED] QM simple harmonic oscillator Homework Statement If I have a particle in an SHO potential and an electric field, I can represent its potential as: V(x) = 0.5 * m \omega^2 (x - \frac{qE}{mw^2})^2 - \frac{1}{2m}(\frac{qE}{\omega})^2 I know the solutions to the TISE...
  8. I

    1-D simple harmonic oscillator

    I was just wondering what the difference was in the 1-D simple harmonic oscillator in the Heisenberg picture versus the Schrodinger picture?
  9. C

    How Is the Angular Frequency of a Bead on a String Calculated?

    The problem is the following: a.) Obtain the equation of motion for the very small oscillations of a bead of mass m attached 1/5th of the way along a massless string of length 5l, which is under tension T. b.) Hence show that the angular frequency of oscillation is omega=sqrt(5T/4ml)...
  10. 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...
  11. 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...
  12. 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...
  13. 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...
  14. 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...
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