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)106 s?

A first-order system G(s) = 0.5/(4s + 1) receives a step input of size 20 at t = 0, starting from rest. Find the output y(6) at t = 6 s.

G(s) = 0.5/(4s + 1)U = 20t = 6 s
y(6) =
2.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 50/(s + 10) receives a step input of size 2 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 50/(s + 10)U = 2
y(∞) =
3.Medium
t (s)y(t)0.5

A system has the transfer function G(s) = 2.5/(s² + 2s + 5) and receives a unit step input. Find the natural frequency ωn in rad/s.

G(s) = 2.5/(s² + 2s + 5)
ωn = rad/s
4.Medium
t (s)y(t)3

A system has the transfer function G(s) = 201/(s² + 6s + 67) and receives a unit step input. Find the natural frequency ωn in rad/s.

G(s) = 201/(s² + 6s + 67)
ωn = rad/s
5.Hard
t (s)y(t)150 %

A second-order system without zeros must have a step response with 50 % overshoot. Find the damping ratio ζ.

%OS = 50 %
ζ =
6.Hard
+−24 VR = 2 ΩL = 10 mHC = 100 µFvC​

A series RLC circuit with R = 2 Ω, L = 10 mH and C = 100 µF is connected to a 24 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the percent overshoot %OS of the capacitor voltage.

R = 2 ΩL = 10 mHC = 100 µFV = 24 V
%OS = %

Answer key

  1. 1. y(6) = 7.769
  2. 2. y(∞) = 10
  3. 3. ωn = 2.236 rad/s
  4. 4. ωn = 8.185 rad/s
  5. 5. ζ = 0.2155
  6. 6. %OS = 72.92 %

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