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
+−5 VR = 100 kΩC = 10 µFvC​

An uncharged capacitor C = 10 µF is charged from a 5 V step source through a resistor R = 100 kΩ. How long after closing the switch does the capacitor voltage reach 60 % of its final value? Find t in ms.

R = 100 kΩC = 10 µFV = 5 V60 %
t = ms
2.Easy
t (s)y(t)y(∞) = ?

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

G(s) = 5/(1s + 1)U = 10
y(∞) =
3.Medium
t (s)y(t)2tp​ = ?

A system has the transfer function G(s) = 110/(s² + 12s + 55) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 110/(s² + 12s + 55)
tp = s
4.Medium
t (s)y(t)0.5tp​ = ?

A system has the transfer function G(s) = 28.5/(s² + 4s + 57) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 28.5/(s² + 4s + 57)
tp = s
5.Hard
t (s)y(t)1tp​ = 1 s4.3 %

The step response of a second-order system without zeros shows 4.3 % overshoot, and the first peak occurs at t = 1 s. Find the natural frequency ωn.

%OS = 4.3 %tp = 1 s
ωn = rad/s
6.Hard
R(s)+225s(s + 16)G(s)C(s)−

A unity negative feedback loop has G(s) = 225/(s(s + 16)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 225/(s(s + 16))
ts = s

Answer key

  1. 1. t = 916.3 ms
  2. 2. y(∞) = 50
  3. 3. tp = 0.7207 s
  4. 4. tp = 0.4315 s
  5. 5. ωn = 4.446 rad/s
  6. 6. ts = 0.5 s

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