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.

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1.Easy
t (s)y(t)25t = ?75 %

A first-order system G(s) = 2.5/(0.5s + 1) receives a step input of size 10 at t = 0, starting from rest. How long does the output take to reach 75 % of its final value? Find t.

G(s) = 2.5/(0.5s + 1)U = 1075 %
t = s
2.Easy
t (s)y(t)100t = ?98 %

A first-order system G(s) = 10/(4s + 1) receives a step input of size 10 at t = 0, starting from rest. How long does the output take to reach 98 % of its final value? Find t.

G(s) = 10/(4s + 1)U = 1098 %
t = s
3.Medium
t (s)y(t)1tp​ = ?

A system has the transfer function G(s) = 23/(s² + 6s + 23) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 23/(s² + 6s + 23)
tp = s
4.Medium
t (s)y(t)1

A system has the transfer function G(s) = 19/(s² + 4s + 19) and receives a unit step input. Find the damping ratio ζ.

G(s) = 19/(s² + 4s + 19)
ζ =
5.Hard
k = 5000 N/mc = 113 N·s/mm = 4 kgF = 5 Nx(t)

A mass m = 4 kg hangs on a spring k = 5000 N/m with a viscous damper c = 113 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 percent overshoot %OS of the displacement.

m = 4 kgk = 5000 N/mc = 113 N·s/mF = 5 N
%OS = %
6.Hard
R(s)+Ks(s + 2)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 2)). Find the gain K that gives a step response with 30 % overshoot.

G(s) = K/(s(s + 2))%OS = 30 %
K =

Answer key

  1. 1. t = 0.6931 s
  2. 2. t = 15.65 s
  3. 3. tp = 0.8396 s
  4. 4. ζ = 0.4588
  5. 5. %OS = 25.43 %
  6. 6. K = 7.809

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