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)y(∞) = ?

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

G(s) = 2/(4s + 1)U = 5
y(∞) =
2.Easy
+−5 VR = 100 kΩC = 47 µFvC​

An uncharged capacitor C = 47 µF is charged from a 5 V step source through a resistor R = 100 kΩ. Find the capacitor voltage vC at t = 3290 ms.

R = 100 kΩC = 47 µFV = 5 Vt = 3290 ms
vC = V
3.Medium
t (s)y(t)2?

A system has the transfer function G(s) = 20/(s² + 3s + 10) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 20/(s² + 3s + 10)
%OS = %
4.Medium
t (s)y(t)2?

A system has the transfer function G(s) = 110/(s² + 6s + 55) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 110/(s² + 6s + 55)
%OS = %
5.Hard
R(s)+Ks(s + 2)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 2)). Find the gain K that gives a step response with 25 % overshoot.

G(s) = K/(s(s + 2))%OS = 25 %
K =
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(∞) = 10
  2. 2. vC = 2.517 V
  3. 3. %OS = 18.4 %
  4. 4. %OS = 24.92 %
  5. 5. K = 6.136
  6. 6. ζ = 0.3579

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