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)1002 s?

A first-order system G(s) = 5/(4s + 1) receives a step input of size 20 at t = 0, starting from rest. Find the output y(2) at t = 2 s.

G(s) = 5/(4s + 1)U = 20t = 2 s
y(2) =
2.Easy
t (s)y(t)10t = ?95 %

A first-order system G(s) = 1/(s + 0.5) receives a step input of size 5 at t = 0, starting from rest. How long does the output take to reach 95 % of its final value? Find t.

G(s) = 1/(s + 0.5)U = 595 %
t = s
3.Medium
t (s)y(t)0.5?

A system has the transfer function G(s) = 35/(s² + 6s + 70) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 35/(s² + 6s + 70)
%OS = %
4.Medium
t (s)y(t)3

A system has the transfer function G(s) = 126/(s² + 5s + 42) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 126/(s² + 5s + 42)
σ =
5.Hard
+−24 VR = 38 ΩL = 10 mHC = 10 µFvC​

A series RLC circuit with R = 38 Ω, L = 10 mH and C = 10 µF is connected to a 24 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the undamped natural frequency ωn in rad/s.

R = 38 ΩL = 10 mHC = 10 µFV = 24 V
ωn = rad/s
6.Hard
t (s)y(t)130 %

A second-order system without zeros must have a step response with 30 % overshoot. Find the damping ratio ζ.

%OS = 30 %
ζ =

Answer key

  1. 1. y(2) = 39.35
  2. 2. t = 5.991 s
  3. 3. %OS = 29.92 %
  4. 4. σ = −2.5
  5. 5. ωn = 3162 rad/s
  6. 6. ζ = 0.3579

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