Step response worksheet with answers

Free printable Step response worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
t (s)y(t)20.16 s?

A first-order system G(s) = 1/(0.8s + 1) receives a step input of size 2 at t = 0, starting from rest. Find the output y(0.16) at t = 0.16 s.

G(s) = 1/(0.8s + 1)U = 2t = 0.16 s
y(0.16) =
2.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 60/(s + 20) receives a step input of size 10 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 60/(s + 20)U = 10
y(∞) =
3.Medium
t (s)y(t)0.5

A system has the transfer function G(s) = 27.5/(s² + 9s + 55) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 27.5/(s² + 9s + 55)
σ =
4.Medium
t (s)y(t)1tp​ = ?

A system has the transfer function G(s) = 31/(s² + 5s + 31) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 31/(s² + 5s + 31)
tp = s
5.Hard
t (s)y(t)120 %

A second-order system without zeros must have a step response with 20 % overshoot. Find the damping ratio ζ.

%OS = 20 %
ζ =
6.Hard
+−5 VR = 28 ΩL = 20 mHC = 1 µFvC​

A series RLC circuit with R = 28 Ω, L = 20 mH and C = 1 µF is connected to a 5 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the time tp of the first voltage peak, in ms.

R = 28 ΩL = 20 mHC = 1 µFV = 5 V
tp = ms

Answer key

  1. 1. y(0.16) = 0.3625
  2. 2. y(∞) = 30
  3. 3. σ = −4.5
  4. 4. tp = 0.6315 s
  5. 5. ζ = 0.4559
  6. 6. tp = 0.4465 ms

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