Poke a system with a sudden change and its damping ratio decides everything — a clean settle, a bouncy overshoot, or a sluggish crawl.
Second-Order Step ResponseLive
damping shapes the response
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A second-order system's response to a step is set entirely by its damping ratio and natural frequency. Low damping overshoots and rings; ζ = 1 is the fastest response without overshoot; high damping is sluggish. Educational tool.
Reading this result: Underdamped: the response overshoots to ~125% of target and rings before settling in about 3.3 s. Lower ζ means bigger overshoot and more oscillation.
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How it works
A second-order system responds to a step according to its damping ratio ζ and natural frequency ωₙ. Overshoot depends only on ζ; settling time scales with 1/(ζωₙ). These metrics are the standard vocabulary of control design. Educational tool.
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The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.