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)100t = ?90 %

A first-order system G(s) = 10/(5s + 1) receives a step input of size 10 at t = 0, starting from rest. How long does the output take to reach 90 % of its final value? Find t.

G(s) = 10/(5s + 1)U = 1090 %
t = s
2.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 4/(0.5s + 1) receives a step input of size 20 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 4/(0.5s + 1)U = 20
y(∞) =
3.Medium
t (s)y(t)2

A system has the transfer function G(s) = 66/(s² + 5s + 33) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 66/(s² + 5s + 33)
σ =
4.Medium
t (s)y(t)2ts​ = ?

A system has the transfer function G(s) = 28/(s² + 4s + 14) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 28/(s² + 4s + 14)
ts = s
5.Hard
R(s)+Ks(s + 8)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 8)). Find the gain K that gives a step response with 2 % overshoot.

G(s) = K/(s(s + 8))%OS = 2 %
K =
6.Hard
k = 2000 N/mc = 57 N·s/mm = 10 kgF = 10 Nx(t)

A mass m = 10 kg hangs on a spring k = 2000 N/m with a viscous damper c = 57 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 10 N is suddenly applied. Find the percent overshoot %OS of the displacement.

m = 10 kgk = 2000 N/mc = 57 N·s/mF = 10 N
%OS = %

Answer key

  1. 1. t = 11.51 s
  2. 2. y(∞) = 80
  3. 3. σ = −2.5
  4. 4. ts = 2 s
  5. 5. K = 26.32
  6. 6. %OS = 52.39 %

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