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)500.01 s?

A first-order system G(s) = 100/(s + 20) receives a step input of size 10 at t = 0, starting from rest. Find the output y(0.01) at t = 0.01 s.

G(s) = 100/(s + 20)U = 10t = 0.01 s
y(0.01) =
2.Easy
t (s)y(t)2t = ?80 %

A first-order system G(s) = 20/(s + 20) receives a step input of size 2 at t = 0, starting from rest. How long does the output take to reach 80 % of its final value? Find t.

G(s) = 20/(s + 20)U = 280 %
t = s
3.Medium
t (s)y(t)2tp​ = ?

A system has the transfer function G(s) = 46/(s² + 2s + 23) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 46/(s² + 2s + 23)
tp = s
4.Medium
t (s)y(t)3ts​ = ?

A system has the transfer function G(s) = 45/(s² + 5s + 15) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 45/(s² + 5s + 15)
ts = s
5.Hard
R(s)+45s(s + 2)G(s)C(s)−

A unity negative feedback loop has G(s) = 45/(s(s + 2)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 45/(s(s + 2))
ts = s
6.Hard
k = 500 N/mc = 13 N·s/mm = 0.5 kgF = 20 Nx(t)

A mass m = 0.5 kg hangs on a spring k = 500 N/m with a viscous damper c = 13 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 20 N is suddenly applied. Find the largest displacement xmax in mm.

m = 0.5 kgk = 500 N/mc = 13 N·s/mF = 20 N
xmax = mm

Answer key

  1. 1. y(0.01) = 9.063
  2. 2. t = 0.08047 s
  3. 3. tp = 0.6698 s
  4. 4. ts = 1.6 s
  5. 5. ts = 4 s
  6. 6. xmax = 49.7 mm

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