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) = 5/(10s + 1) receives a step input of size 20 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 5/(10s + 1)U = 20
y(∞) =
2.Easy
t (s)y(t)20t = ?50 %

A first-order system G(s) = 1/(5s + 1) receives a step input of size 20 at t = 0, starting from rest. How long does the output take to reach 50 % of its final value? Find t.

G(s) = 1/(5s + 1)U = 2050 %
t = s
3.Medium
t (s)y(t)2tp​ = ?

A system has the transfer function G(s) = 8/(s² + 3s + 4) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 8/(s² + 3s + 4)
tp = s
4.Medium
t (s)y(t)1ts​ = ?

A system has the transfer function G(s) = 99/(s² + 14s + 99) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 99/(s² + 14s + 99)
ts = s
5.Hard
t (s)y(t)125 %

A second-order system without zeros must have a step response with 25 % overshoot. Find the damping ratio ζ.

%OS = 25 %
ζ =
6.Hard
k = 5000 N/mc = 63 N·s/mm = 5 kgF = 50 Nx(t)

A mass m = 5 kg hangs on a spring k = 5000 N/m with a viscous damper c = 63 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 50 N is suddenly applied. Find the percent overshoot %OS of the displacement.

m = 5 kgk = 5000 N/mc = 63 N·s/mF = 50 N
%OS = %

Answer key

  1. 1. y(∞) = 100
  2. 2. t = 3.466 s
  3. 3. tp = 2.375 s
  4. 4. ts = 0.5714 s
  5. 5. ζ = 0.4037
  6. 6. %OS = 52.8 %

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