Spring Oscillation

Explore damped, undamped, forced, and unforced spring oscillation.

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Question

How do damping and an outside force change the motion of a spring?

The same spring equation produces very different motion as its forces change.
The same spring equation produces very different motion as its forces change.

Goals

  • Compare damped, undamped, forced, and unforced oscillations.
  • Connect the model parameters with graphs and animated motion.

Method

Start from the balance of mass, damping, spring, and external forces.

  • Use the equation \(m x''+c x'+kx=F(t)\) to describe displacement.
  • Solve selected cases by hand or compute them numerically.
  • Plot or animate the motion while changing mass, damping, stiffness, and forcing.

Try an example

Spring!

Source code ↗ Open full screen ↗

Change damping and periodic forcing, then compare the moving mass with its displacement trace.

Controls: Use the DAMP and FORCE buttons to change the model. Press R or click RESET to restart the motion.