Double-spring Motion

Model the coupled motion of two springs.

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Learn Mathematics Differential Equations

Question

How does motion pass between two masses joined by springs?

Goals

  • Derive a coupled system for the two displacements.
  • Find and visualize normal modes and more general motions.

Method

Describe how the force on each mass depends on both positions.

  • Draw a force diagram and write the two coupled differential equations.
  • Express the system with matrices and solve it through eigenmodes or numerical steps.
  • Animate both masses and compare motion from different starting positions.

Try an example

Set two masses, two spring constants, and four initial values. The exact modal solution drives both the moving spring system and the two displacement traces.

Controls: Choose a motion preset or enter your own values, then select Apply & run. Use Space to pause, R to restart, or drag the time control.