Second-Order ResponseNatural frequency sets the speed, damping ratio sets the overshoot.Mechanical EngineeringTwo numbers describe it: natural frequency sets thespeed and damping ratio sets the overshoot.ωn² ÷ (s² + 2 zeta ωn s + ωn²) · zeta = damping ratiozeta = 0.7About 5% overshootA common target.zeta = 0.5About 16% overshootFaster, less damped.zeta = 0.7, ωn = 10Settles in about 0.6 sRoughly 4 ÷ zeta ωn.THE COMMON MISTAKE✗ Raising the gain to make it faster✓ Gain raises ωn and cuts dampingIn most loops more gain means more overshoot and less margin. Speed anddamping trade against each other unless you add derivative action.Underdamped means damping ratio below one. At exactly one theresponse is critically damped, the fastest with no overshoot.Second-Order Responselearnposters.com
Second-Order Response — printable engineering wall chart from LearnPosters. Free vector PDF, US Letter and A4.

What’s on the Second-Order Response poster

The rule, 3 worked examples, and the mistake everyone makes.

Underdamped means damping ratio below one. At exactly one the response is critically damped, the fastest with no overshoot.

Questions about the Second-Order Response poster

What’s on the Second-Order Response poster?
The rule, 3 worked examples, and the mistake everyone makes. Two numbers describe it: natural frequency sets the speed and damping ratio sets the…; ωn² ÷ (s² + 2 zeta ωn s + ωn²) · zeta = damping ratio; zeta = 0.7 = About 5% overshoot; zeta = 0.5 = About 16% overshoot; zeta = 0.7, ωn = 10 = Settles in about 0.6 s; Common mistake: Raising the gain to make it faster → Gain raises ωn and cuts damping. Underdamped means damping ratio below one. At exactly one the response is critically damped, the fastest with no overshoot.
Who is the Second-Order Response poster for?
Second-Order Response belongs to the Mechanical Engineering section rather than to a school year, because engineering is not something one grade owns. Anyone learning control systems can pin it up — a beginner, a student mid-course, or someone revising years later.
When should you use the Second-Order Response poster?
Tuning any loop that rings, or specifying an overshoot and settling target. A wall chart earns its place by being glanceable from where the work is happening, so Second-Order Response belongs on the wall where that engineering work actually happens, within glancing distance, rather than filed away.
What other posters go with Second-Order Response?
Block Diagram Algebra, Gain & Phase Margin and First-Order Response sit alongside Second-Order Response in the Mechanical Engineering section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Block Diagram AlgebraGain & Phase MarginFirst-Order Response
Is the Second-Order Response poster free to download and print?
Yes. Second-Order Response downloads as a free PDF with no account, no email and no watermark, like everything else in the Mechanical Engineering section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
What size does the Second-Order Response poster print at?
Second-Order Response is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Second-Order Response loses nothing.Printing guide

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