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)y(∞) = ?

A first-order system G(s) = 10/(0.2s + 1) receives a step input of size 5 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 10/(0.2s + 1)U = 5
y(∞) =
2.Easy
t (s)y(t)5010 s45

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 50. At t = 10 s it reads 45. Find the time constant τ.

y(∞) = 50y(10) = 45
τ = s
3.Medium
t (s)y(t)0.5tp​ = ?

A system has the transfer function G(s) = 37/(s² + 6s + 74) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 37/(s² + 6s + 74)
tp = s
4.Medium
t (s)y(t)2?

A system has the transfer function G(s) = 12/(s² + 3s + 6) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 12/(s² + 3s + 6)
%OS = %
5.Hard
R(s)+80s(s + 2)G(s)C(s)−

A unity negative feedback loop has G(s) = 80/(s(s + 2)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 80/(s(s + 2))
ts = s
6.Hard
k = 400 N/mc = 32 N·s/mm = 2.5 kgF = 5 Nx(t)

A mass m = 2.5 kg hangs on a spring k = 400 N/m with a viscous damper c = 32 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 5 N is suddenly applied. Find the damping ratio ζ.

m = 2.5 kgk = 400 N/mc = 32 N·s/mF = 5 N
ζ =

Answer key

  1. 1. y(∞) = 50
  2. 2. τ = 4.343 s
  3. 3. tp = 0.3897 s
  4. 4. %OS = 8.773 %
  5. 5. ts = 4 s
  6. 6. ζ = 0.506

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