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)203 s18

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 20. At t = 3 s it reads 18. Find the time constant τ.

y(∞) = 20y(3) = 18
τ = s
2.Easy
+−5 VR = 10 kΩC = 1 µFvC​

An uncharged capacitor C = 1 µF is charged from a 5 V step source through a resistor R = 10 kΩ. How long after closing the switch does the capacitor voltage reach 60 % of its final value? Find t in ms.

R = 10 kΩC = 1 µFV = 5 V60 %
t = ms
3.Medium
t (s)y(t)3

A system has the transfer function G(s) = 117/(s² + 9s + 39) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 117/(s² + 9s + 39)
σ =
4.Medium
t (s)y(t)0.5

A system has the transfer function G(s) = 35.5/(s² + 10s + 71) and receives a unit step input. Find the damping ratio ζ.

G(s) = 35.5/(s² + 10s + 71)
ζ =
5.Hard
R(s)+160s(s + 4)G(s)C(s)−

A unity negative feedback loop has G(s) = 160/(s(s + 4)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 160/(s(s + 4))
ts = s
6.Hard
R(s)+Ks(s + 4)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 4)). Find the gain K that gives a step response with 20 % overshoot.

G(s) = K/(s(s + 4))%OS = 20 %
K =

Answer key

  1. 1. τ = 1.303 s
  2. 2. t = 9.163 ms
  3. 3. σ = −4.5
  4. 4. ζ = 0.5934
  5. 5. ts = 2 s
  6. 6. K = 19.24

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