Turn up the feedback gain and watch a system's poles march across the complex plane — straight toward instability if you push too far.
Root LocusLive
how poles move with gain
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The root locus traces where a system's closed-loop poles travel as feedback gain increases. Poles in the left half-plane mean stability; as gain rises they migrate toward the imaginary axis, and crossing it triggers oscillation. Educational tool.
Reading this result: Gain K=3 sits below the breakaway value, so both closed-loop poles stay real and negative near -2.00 — the response is overdamped with no oscillation.
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How it works
The root locus plots how closed-loop pole locations change as loop gain varies from zero to infinity. Poles in the left half-plane are stable; as gain increases they move toward and may cross the imaginary axis, marking the onset of sustained oscillation. 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.