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)10t = ?80 %

A first-order system G(s) = 0.5/(s + 0.5) receives a step input of size 10 at t = 0, starting from rest. How long does the output take to reach 80 % of its final value? Find t.

G(s) = 0.5/(s + 0.5)U = 1080 %
t = s
2.Easy
t (s)y(t)205 s16

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 20. At t = 5 s it reads 16. Find the time constant τ.

y(∞) = 20y(5) = 16
τ = s
3.Medium
t (s)y(t)0.5tp​ = ?

A system has the transfer function G(s) = 3.5/(s² + 2s + 7) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 3.5/(s² + 2s + 7)
tp = s
4.Medium
t (s)y(t)1tp​ = ?

A system has the transfer function G(s) = 40/(s² + 10s + 40) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 40/(s² + 10s + 40)
tp = s
5.Hard
t (s)y(t)140 %

A second-order system without zeros must have a step response with 40 % overshoot. Find the damping ratio ζ.

%OS = 40 %
ζ =
6.Hard
+−12 VR = 17 ΩL = 20 mHC = 100 µFvC​

A series RLC circuit with R = 17 Ω, L = 20 mH and C = 100 µF is connected to a 12 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the peak capacitor voltage vC,max.

R = 17 ΩL = 20 mHC = 100 µFV = 12 V
vC,max = V

Answer key

  1. 1. t = 3.219 s
  2. 2. τ = 3.107 s
  3. 3. tp = 1.283 s
  4. 4. tp = 0.8112 s
  5. 5. ζ = 0.28
  6. 6. vC,max = 13.13 V

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