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)0.50.025 s?

A first-order system G(s) = 10/(s + 20) receives a step input of size 1 at t = 0, starting from rest. Find the output y(0.025) at t = 0.025 s.

G(s) = 10/(s + 20)U = 1t = 0.025 s
y(0.025) =
2.Easy
t (s)y(t)50.4 s?

A first-order system G(s) = 0.5/(0.2s + 1) receives a step input of size 10 at t = 0, starting from rest. Find the output y(0.4) at t = 0.4 s.

G(s) = 0.5/(0.2s + 1)U = 10t = 0.4 s
y(0.4) =
3.Medium
t (s)y(t)3?

A system has the transfer function G(s) = 102/(s² + 7s + 34) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 102/(s² + 7s + 34)
%OS = %
4.Medium
t (s)y(t)1?

A system has the transfer function G(s) = 38/(s² + 2s + 38) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 38/(s² + 2s + 38)
%OS = %
5.Hard
R(s)+Ks(s + 12)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 12)). Find the gain K that gives a step response with 5 % overshoot.

G(s) = K/(s(s + 12))%OS = 5 %
K =
6.Hard
k = 100 N/mc = 8 N·s/mm = 8 kgF = 10 Nx(t)

A mass m = 8 kg hangs on a spring k = 100 N/m with a viscous damper c = 8 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 10 N is suddenly applied. Find the time tp at which the displacement is largest.

m = 8 kgk = 100 N/mc = 8 N·s/mF = 10 N
tp = s

Answer key

  1. 1. y(0.025) = 0.1967
  2. 2. y(0.4) = 4.323
  3. 3. %OS = 9.464 %
  4. 4. %OS = 59.66 %
  5. 5. K = 75.59
  6. 6. tp = 0.8976 s

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