FirstPrinciplesa Physoly project
SHM-04wavestrap · Force / acceleration confusion

Mass-spring period does not depend on amplitude

  1. 01

    The tempting model

    Assuming a larger oscillation must take longer because it travels farther.

  2. 02

    Why it feels right

    More distance usually means more time.

  3. 03

    Where it breaks · how to catch it

    You put amplitude A into T = 2π √(m/k) for an ideal spring.

  4. 04

    The correct model

    For ideal SHM, larger amplitude also gives larger maximum speed. The period T = 2π √(m/k) is independent of amplitude.

  5. 05

    Repair · see it, then test it

    worked example A spring oscillator's amplitude doubles. What happens to its period?

    Tempting move

    It doubles.

    Correct move

    It stays the same in the ideal SHM model.

    Test the repair SHM-04 · transfer
    The amplitude of an ideal mass-spring oscillator is tripled without changing m or k. Its period:

    Make a fresh prediction before referring to the worked example.