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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
t (s)y(t)0.55 s?

A first-order system G(s) = 0.5/(10s + 1) receives a step input of size 1 at t = 0, starting from rest. Find the output y(5) at t = 5 s.

G(s) = 0.5/(10s + 1)U = 1t = 5 s
y(5) =
2.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 10/(10s + 1) receives a step input of size 2 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 10/(10s + 1)U = 2
y(∞) =
3.Medium
t (s)y(t)2tp​ = ?

A system has the transfer function G(s) = 152/(s² + 12s + 76) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 152/(s² + 12s + 76)
tp = s
4.Medium
t (s)y(t)0.5tp​ = ?

A system has the transfer function G(s) = 37.5/(s² + 9s + 75) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 37.5/(s² + 9s + 75)
tp = s
5.Hard
+−5 VR = 48 ΩL = 50 mHC = 22 µFvC​

A series RLC circuit with R = 48 Ω, L = 50 mH and C = 22 µF is connected to a 5 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the time tp of the first voltage peak, in ms.

R = 48 ΩL = 50 mHC = 22 µFV = 5 V
tp = ms
6.Hard
R(s)+Ks(s + 20)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 20)). Find the gain K that gives a step response with 20 % overshoot.

G(s) = K/(s(s + 20))%OS = 20 %
K =

Answer key

  1. 1. y(5) = 0.1967
  2. 2. y(∞) = 20
  3. 3. tp = 0.4967 s
  4. 4. tp = 0.4246 s
  5. 5. tp = 3.813 ms
  6. 6. K = 481

Full step-by-step solutions: practise this topic on examproblems.com.