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

G(s) = 20/(s + 20)U = 20
y(∞) =
2.Easy
t (s)y(t)31 s?

A first-order system G(s) = 6/(s + 2) receives a step input of size 1 at t = 0, starting from rest. Find the output y(1) at t = 1 s.

G(s) = 6/(s + 2)U = 1t = 1 s
y(1) =
3.Medium
t (s)y(t)2?

A system has the transfer function G(s) = 94/(s² + 4s + 47) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 94/(s² + 4s + 47)
%OS = %
4.Medium
t (s)y(t)3tp​ = ?

A system has the transfer function G(s) = 75/(s² + 6s + 25) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 75/(s² + 6s + 25)
tp = s
5.Hard
R(s)+Ks(s + 12)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 12)). Find the gain K that gives a step response with 2 % overshoot.

G(s) = K/(s(s + 12))%OS = 2 %
K =
6.Hard
k = 5000 N/mc = 120 N·s/mm = 8 kgF = 100 Nx(t)

A mass m = 8 kg hangs on a spring k = 5000 N/m with a viscous damper c = 120 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 time tp at which the displacement is largest.

m = 8 kgk = 5000 N/mc = 120 N·s/mF = 100 N
tp = s

Answer key

  1. 1. y(∞) = 20
  2. 2. y(1) = 2.594
  3. 3. %OS = 38.36 %
  4. 4. tp = 0.7854 s
  5. 5. K = 59.22
  6. 6. tp = 0.1317 s

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