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)82 s5.6

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 8. At t = 2 s it reads 5.6. Find the time constant τ.

y(∞) = 8y(2) = 5.6
τ = s
2.Easy
t (s)y(t)6t = ?90 %

A first-order system G(s) = 15/(s + 5) receives a step input of size 2 at t = 0, starting from rest. How long does the output take to reach 90 % of its final value? Find t.

G(s) = 15/(s + 5)U = 290 %
t = s
3.Medium
t (s)y(t)3

A system has the transfer function G(s) = 144/(s² + 11s + 48) and receives a unit step input. Find the natural frequency ωn in rad/s.

G(s) = 144/(s² + 11s + 48)
ωn = rad/s
4.Medium
t (s)y(t)1tp​ = ?

A system has the transfer function G(s) = 40/(s² + 6s + 40) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 40/(s² + 6s + 40)
tp = s
5.Hard
+−10 VR = 190 ΩL = 100 mHC = 1 µFvC​

A series RLC circuit with R = 190 Ω, L = 100 mH and C = 1 µF is connected to a 10 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the peak capacitor voltage vC,max.

R = 190 ΩL = 100 mHC = 1 µFV = 10 V
vC,max = V
6.Hard
t (s)y(t)1tp​ = 0.5 s50 %

The step response of a second-order system without zeros shows 50 % overshoot, and the first peak occurs at t = 0.5 s. Find the natural frequency ωn.

%OS = 50 %tp = 0.5 s
ωn = rad/s

Answer key

  1. 1. τ = 1.661 s
  2. 2. t = 0.4605 s
  3. 3. ωn = 6.928 rad/s
  4. 4. tp = 0.5642 s
  5. 5. vC,max = 13.72 V
  6. 6. ωn = 6.434 rad/s

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