MAE 4182 · Tuesday, October 20, 2026 · Narrated lesson

Root Locus → Frequency Response
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Read two root-locus plots

Play the explanation → try the task → click Next to check. You can pause, replay, or move on anytime.

Monday ended after choosing K; pause and read these two plots.

A. Can a larger K make it unstable?

Loop model L(s) · Read the supplied plot.

L(s) = 1s[(s + 4)² + 16]

0 < K < 256: stable?

K = 256: does the transient decay?

K > 256: stable?

Root locus of one over s times the quantity s plus four squared plus sixteenThree branches start at zero and minus four plus or minus four j. One moves left along the real axis. The conjugate pair moves toward the right half-plane and crosses the imaginary axis at plus or minus j square root of 32 when K equals 256. The shaded right half-plane is unstable. Arrowheads show increasing K; all three branches continue to infinity. Equal real and imaginary scales.-12-8-404-8j-4j4j8jReIm−4 + j4−4 − j4K = 256±j√32Re > 0unstable× open-loop polesarrows: increasing K
Start: three open-loop poles

K changes; the plant is unchanged.

Your turnClick K = 40, K = 256, and K = 400. Track every pole.
Synthetic English narration
Transcript

This is the narrated version of Tuesday's lecture, using a synthetic voice. We begin where Monday stopped: reading root-locus plots. The horizontal axis is the real part, not time. Each moving dot is a closed-loop pole. Use the gain controls to compare values below, at, and above 256. Look at every pole, not just one. Does the transient decay, persist, or grow? Try the animation and predict before continuing. Predict decay, persistence, or growth for each; then click Next step at the bottom.

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