FirstPrinciplesa Physoly project
SHM-03wavestrap · Force / acceleration confusion

In SHM, velocity and acceleration peak a quarter-cycle apart

  1. 01

    The tempting model

    Assuming a mass on a spring is fastest where its acceleration is greatest.

  2. 02

    Why it feels right

    It seems the biggest push should coincide with the biggest speed.

  3. 03

    Where it breaks · how to catch it

    You placed peak speed and peak acceleration at the same point.

  4. 04

    The correct model

    Model SHM as a rotating phasor: x = A sin ωt, v leads by 90°, and a is opposite x. Speed peaks at the center (a = 0); acceleration peaks at the extremes (v = 0).

  5. 05

    Repair · see it, then test it

    worked example Where is a mass on a spring moving fastest?

    Tempting move

    At the extreme, where the force is largest.

    Correct move

    At equilibrium, where acceleration is zero.

    Test the repair SHM-03 · transfer
    As an ideal spring oscillator passes through equilibrium, which pair is correct?

    Make a fresh prediction before referring to the worked example.