In pure modes spring force is ±90 degrees out of phase with velocity

Evidence

Inspection of the higher frequency mode for any length of the red pendulum (see the short green dashed lines in figure 10.7) shows that maximum force (minimum or maximum spring extension) is always associated with zero velocity, with force leading velocity by +90 degrees. The lower frequency curve reveals that that maximum force (minimum or maximum spring extension) is also associated with zero velocity, this time with a –90 degrees lag on the force. — Eric J. Heller, Why You Hear What You Hear- An…, 1037

Categorization

• DEFINE: Explains why no energy is exchanged between oscillators in a pure mode: the force-velocity phase relation means zero net work over a cycle.