Three degrees of damping
● VERBATIM — examined word-for-wordLight: still oscillates; amplitude decays exponentially (constant fraction lost per cycle); period almost unchanged. Critical: returns to equilibrium in the shortest time without oscillating — car suspension, meter needles. Heavy: returns slowly, no oscillation. Sketch tip: exponential envelope, but zero-crossings stay equally spaced.
What this actually means
Light damping: the system still oscillates, the amplitude decays exponentially (a constant fraction lost each cycle), and the period is almost unchanged.
Critical damping: the system returns to equilibrium in the shortest possible time WITHOUT oscillating. This is the engineered sweet spot: car suspension, meter needles.
Heavy damping: no oscillation either, but a slow crawl back. Sketch discipline: draw the exponential envelope, and keep the zero crossings equally spaced even as the peaks shrink.
Calling heavy damping the fastest return — critical damping returns in the shortest time without oscillating.
Prove it — watch it be true
- Open free damping and run light: decaying oscillation inside an exponential envelope
- Run critical: straight home in the shortest time, no overshoot
- Run heavy: still no overshoot, but a visibly slower return