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)45 s2.4

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 4. At t = 5 s it reads 2.4. Find the time constant τ.

y(∞) = 4y(5) = 2.4
τ = s
2.Easy
t (s)y(t)80.8 s?

A first-order system G(s) = 4/(0.8s + 1) receives a step input of size 2 at t = 0, starting from rest. Find the output y(0.8) at t = 0.8 s.

G(s) = 4/(0.8s + 1)U = 2t = 0.8 s
y(0.8) =
3.Medium
t (s)y(t)3tp​ = ?

A system has the transfer function G(s) = 42/(s² + 3s + 14) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 42/(s² + 3s + 14)
tp = s
4.Medium
t (s)y(t)0.5?

A system has the transfer function G(s) = 4/(s² + 2s + 8) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 4/(s² + 2s + 8)
%OS = %
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 = 400 N/mc = 27 N·s/mm = 5 kgF = 10 Nx(t)

A mass m = 5 kg hangs on a spring k = 400 N/m with a viscous damper c = 27 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 largest displacement xmax in mm.

m = 5 kgk = 400 N/mc = 27 N·s/mF = 10 N
xmax = mm

Answer key

  1. 1. τ = 5.457 s
  2. 2. y(0.8) = 5.057
  3. 3. tp = 0.9165 s
  4. 4. %OS = 30.5 %
  5. 5. K = 26.32
  6. 6. xmax = 34.25 mm

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