9860

Energy and Position Relationships in Simple Harmonic Motion

In simple harmonic motion, when a particle of mass is displaced from its equilibrium position, it experiences a restoring force proportional to its displacement (Hooke's law). The resultant motion produces a sinusoidal curve for the displacement as a function of time, and it interconverts potential energy (PE) and kinetic energy (KE) in a periodic manner (while keeping total energy constant). Interactivity involves the effects of the total energy and force constant on the potential energy well, displacement, and potential and kinetic energies of a simple harmonic oscillator, and also includes the ability to track energies and position as a function of time.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

The first control lets you select the total energy of the harmonic oscillator. For the plot of potential energy as a function of displacement, this will move the red point and level to the appropriate position on the potential energy well and the other plots will change accordingly. The second control lets you select the force constant, essentially increasing or decreasing the strength of the spring. The final control manipulates time. The mass on the spring and the red points track displacement as a function of time, the blue points track potential energy as a function of time, and the green point tracks kinetic energy as a function of time.
Snapshot 1: at time zero, the harmonic oscillator is in its equilibrium position with maximum kinetic energy and zero potential energy
Snapshot 2: at maximum displacement from equilibrium, the harmonic oscillator has zero kinetic energy and maximum potential energy
Snapshot 3: an increase in the total energy of the harmonic oscillator also increases the amplitude of displacement
Snapshot 4: an increase in the force constant of the spring narrows the potential energy well, increasing the frequency of oscillation
Reference:
P. Atkins and J. de Paula, Physical Chemistry, New York: Oxford University Press, 2006.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+