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)0.5t = ?99 %

A first-order system G(s) = 0.5/(10s + 1) receives a step input of size 1 at t = 0, starting from rest. How long does the output take to reach 99 % of its final value? Find t.

G(s) = 0.5/(10s + 1)U = 199 %
t = s
2.Easy
t (s)y(t)25t = ?60 %

A first-order system G(s) = 50/(s + 10) receives a step input of size 5 at t = 0, starting from rest. How long does the output take to reach 60 % of its final value? Find t.

G(s) = 50/(s + 10)U = 560 %
t = s
3.Medium
t (s)y(t)3?

A system has the transfer function G(s) = 147/(s² + 7s + 49) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 147/(s² + 7s + 49)
%OS = %
4.Medium
t (s)y(t)0.5tp​ = ?

A system has the transfer function G(s) = 10.5/(s² + 3s + 21) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 10.5/(s² + 3s + 21)
tp = s
5.Hard
t (s)y(t)150 %

A second-order system without zeros must have a step response with 50 % overshoot. Find the damping ratio ζ.

%OS = 50 %
ζ =
6.Hard
k = 200 N/mc = 11 N·s/mm = 4 kgF = 100 Nx(t)

A mass m = 4 kg hangs on a spring k = 200 N/m with a viscous damper c = 11 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 100 N is suddenly applied. Find the percent overshoot %OS of the displacement.

m = 4 kgk = 200 N/mc = 11 N·s/mF = 100 N
%OS = %

Answer key

  1. 1. t = 46.05 s
  2. 2. t = 0.09163 s
  3. 3. %OS = 16.3 %
  4. 4. tp = 0.7255 s
  5. 5. ζ = 0.2155
  6. 6. %OS = 53.64 %

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