Coupled Oscillators and Normal Modes · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Two masses, two favourite dances

Science · Forces & Motion · ages 19-20
Name ______________________   Date ____________
  1. Which normal mode runs faster?

    • The out of phase mode
    • The in phase mode
    • Both run at the same speed
  2. Two masses joined by springs settle into a normal mode. What is happening?

    • Each mass swings at its own private frequency
    • Whole system in one pattern at one frequency
    • Both masses sit still while the springs swing
  3. Why does the out of phase mode run faster?

    • The masses become heavier
    • Coupling spring pulls more
    • The outer springs go slack
  4. You start the system in a mixture of both modes. What does the energy do?

    • It vanishes at once
    • It stays locked in one mass
    • It sloshes back and forth between the masses
  5. You displace both masses equally in the same direction and let go. What follows?

    • Pure in phase motion at the slower frequency
    • Pure out of phase motion at the faster frequency
    • Both masses freeze at the release point
  6. Any starting motion of the two masses can be written as a sum of the two normal modes.

    Circle one:   True   False

  7. You pull only one mass aside and release. What motion follows?

    • Both modes excited, with energy beating across
    • Pure in phase motion only
    • No motion at all
  8. Kim watches one mode and says each mass swings at its own frequency. What is wrong?

    • Modes only exist with damping
    • Frequency belongs to the whole pattern, not each mass
    • In phase motion has no frequency
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Two masses, two favourite dances W1-mt_vnTGOIqZzP-s1

  1. The out of phase mode · Opposite motion stretches the coupling spring extra.
  2. Whole system in one pattern at one frequency · A mode is one pattern of the entire system.
  3. Coupling spring pulls more · Extra stretch means extra restoring pull each cycle.
  4. It sloshes back and forth between the masses · The two frequencies beat, sending energy across and back.
  5. Pure in phase motion at the slower frequency · That start matches the in phase pattern exactly.
  6. True · The start sets the weights, and the modes span every motion.
  7. Both modes excited, with energy beating across · A one-sided start matches neither pattern, so both join in.
  8. Frequency belongs to the whole pattern, not each mass · In a mode the entire pattern shares a single frequency.
Worksheet · LightMySky