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)2t = ?75 %

A first-order system G(s) = 2/(s + 1) receives a step input of size 1 at t = 0, starting from rest. How long does the output take to reach 75 % of its final value? Find t.

G(s) = 2/(s + 1)U = 175 %
t = s
2.Easy
+−10 VR = 100 kΩC = 4.7 µFvC​

An uncharged capacitor C = 4.7 µF is charged from a 10 V step source through a resistor R = 100 kΩ. How long after closing the switch does the capacitor voltage reach 99 % of its final value? Find t in ms.

R = 100 kΩC = 4.7 µFV = 10 V99 %
t = ms
3.Medium
t (s)y(t)3tp​ = ?

A system has the transfer function G(s) = 87/(s² + 5s + 29) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 87/(s² + 5s + 29)
tp = s
4.Medium
t (s)y(t)2?

A system has the transfer function G(s) = 190/(s² + 12s + 95) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 190/(s² + 12s + 95)
%OS = %
5.Hard
+−12 VR = 26 ΩL = 200 mHC = 47 µFvC​

A series RLC circuit with R = 26 Ω, L = 200 mH and C = 47 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 = 26 ΩL = 200 mHC = 47 µFV = 12 V
vC,max = V
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. t = 1.386 s
  2. 2. t = 2164 ms
  3. 3. tp = 0.6587 s
  4. 4. %OS = 8.595 %
  5. 5. vC,max = 18.33 V
  6. 6. ζ = 0.3579

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