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)250.3 s?

A first-order system G(s) = 25/(s + 5) receives a step input of size 5 at t = 0, starting from rest. Find the output y(0.3) at t = 0.3 s.

G(s) = 25/(s + 5)U = 5t = 0.3 s
y(0.3) =
2.Easy
t (s)y(t)200.5 s?

A first-order system G(s) = 1/(0.5s + 1) receives a step input of size 20 at t = 0, starting from rest. Find the output y(0.5) at t = 0.5 s.

G(s) = 1/(0.5s + 1)U = 20t = 0.5 s
y(0.5) =
3.Medium
t (s)y(t)0.5ts​ = ?

A system has the transfer function G(s) = 29/(s² + 9s + 58) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 29/(s² + 9s + 58)
ts = s
4.Medium
t (s)y(t)1?

A system has the transfer function G(s) = 19/(s² + 3s + 19) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 19/(s² + 3s + 19)
%OS = %
5.Hard
k = 800 N/mc = 8 N·s/mm = 1 kgF = 100 Nx(t)

A mass m = 1 kg hangs on a spring k = 800 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 = 100 N is suddenly applied. Find the percent overshoot %OS of the displacement.

m = 1 kgk = 800 N/mc = 8 N·s/mF = 100 N
%OS = %
6.Hard
t (s)y(t)18 %

A second-order system without zeros must have a step response with 8 % overshoot. Find the damping ratio ζ.

%OS = 8 %
ζ =

Answer key

  1. 1. y(0.3) = 19.42
  2. 2. y(0.5) = 12.64
  3. 3. ts = 0.8889 s
  4. 4. %OS = 31.62 %
  5. 5. %OS = 63.84 %
  6. 6. ζ = 0.6266

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