कला मार्जिन कैलकुलेटर — सूत्र

Damping Ratio from Overshoot

The damping ratio determines the character of a second-order system response. It can be extracted from a measured step response by noting the percent overshoot.

Formula

zeta = ln(%OS/100) / sqrt(pi² + ln²(%OS/100))

  • zeta < 1: underdamped (oscillatory)
  • zeta = 1: critically damped (fastest non-oscillatory)
  • zeta > 1: overdamped (sluggish, no oscillations)

    • हल किया गया उदाहरण

    A step response shows 20% overshoot.

    1. ln(0.20) = -1.6094
    2. zeta = 1.6094 / sqrt(9.8696 + 2.5902)
    3. zeta = 1.6094 / sqrt(12.4598) = 1.6094 / 3.5299
    4. zeta = 0.4559