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)40.8 s?

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

G(s) = 4/(4s + 1)U = 1t = 0.8 s
y(0.8) =
2.Easy
t (s)y(t)20.7 s?

A first-order system G(s) = 1/(1s + 1) receives a step input of size 2 at t = 0, starting from rest. Find the output y(0.7) at t = 0.7 s.

G(s) = 1/(1s + 1)U = 2t = 0.7 s
y(0.7) =
3.Medium
t (s)y(t)2?

A system has the transfer function G(s) = 178/(s² + 7s + 89) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 178/(s² + 7s + 89)
%OS = %
4.Medium
t (s)y(t)3ts​ = ?

A system has the transfer function G(s) = 288/(s² + 9s + 96) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 288/(s² + 9s + 96)
ts = s
5.Hard
k = 100 N/mc = 12 N·s/mm = 1 kgF = 5 Nx(t)

A mass m = 1 kg hangs on a spring k = 100 N/m with a viscous damper c = 12 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 percent overshoot %OS of the displacement.

m = 1 kgk = 100 N/mc = 12 N·s/mF = 5 N
%OS = %
6.Hard
R(s)+210s(s + 10)G(s)C(s)−

A unity negative feedback loop has G(s) = 210/(s(s + 10)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 210/(s(s + 10))
ts = s

Answer key

  1. 1. y(0.8) = 0.7251
  2. 2. y(0.7) = 1.007
  3. 3. %OS = 28.5 %
  4. 4. ts = 0.8889 s
  5. 5. %OS = 9.478 %
  6. 6. ts = 0.8 s

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