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)y(∞) = ?

A first-order system G(s) = 2.5/(0.8s + 1) receives a step input of size 10 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 2.5/(0.8s + 1)U = 10
y(∞) =
2.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 2/(2s + 1) receives a step input of size 2 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 2/(2s + 1)U = 2
y(∞) =
3.Medium
t (s)y(t)0.5tp​ = ?

A system has the transfer function G(s) = 38/(s² + 3s + 76) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 38/(s² + 3s + 76)
tp = s
4.Medium
t (s)y(t)0.5tp​ = ?

A system has the transfer function G(s) = 45/(s² + 9s + 90) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 45/(s² + 9s + 90)
tp = s
5.Hard
k = 400 N/mc = 38 N·s/mm = 10 kgF = 5 Nx(t)

A mass m = 10 kg hangs on a spring k = 400 N/m with a viscous damper c = 38 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 largest displacement xmax in mm.

m = 10 kgk = 400 N/mc = 38 N·s/mF = 5 N
xmax = mm
6.Hard
t (s)y(t)1tp​ = 1 s20 %

The step response of a second-order system without zeros shows 20 % overshoot, and the first peak occurs at t = 1 s. Find the natural frequency ωn.

%OS = 20 %tp = 1 s
ωn = rad/s

Answer key

  1. 1. y(∞) = 25
  2. 2. y(∞) = 4
  3. 3. tp = 0.3658 s
  4. 4. tp = 0.3762 s
  5. 5. xmax = 17.15 mm
  6. 6. ωn = 3.53 rad/s

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