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)2.50.6 s?

A first-order system G(s) = 2.5/(s + 5) receives a step input of size 5 at t = 0, starting from rest. Find the output y(0.6) at t = 0.6 s.

G(s) = 2.5/(s + 5)U = 5t = 0.6 s
y(0.6) =
2.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 2.5/(0.8s + 1) receives a step input of size 5 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 2.5/(0.8s + 1)U = 5
y(∞) =
3.Medium
t (s)y(t)2tp​ = ?

A system has the transfer function G(s) = 14/(s² + 4s + 7) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 14/(s² + 4s + 7)
tp = s
4.Medium
t (s)y(t)3?

A system has the transfer function G(s) = 48/(s² + 4s + 16) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 48/(s² + 4s + 16)
%OS = %
5.Hard
k = 200 N/mc = 6 N·s/mm = 5 kgF = 50 Nx(t)

A mass m = 5 kg hangs on a spring k = 200 N/m with a viscous damper c = 6 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 = 200 N/mc = 6 N·s/mF = 50 N
%OS = %
6.Hard
t (s)y(t)1tp​ = 0.2 s5 %

The step response of a second-order system without zeros shows 5 % overshoot, and the first peak occurs at t = 0.2 s. Find the natural frequency ωn.

%OS = 5 %tp = 0.2 s
ωn = rad/s

Answer key

  1. 1. y(0.6) = 2.376
  2. 2. y(∞) = 12.5
  3. 3. tp = 1.814 s
  4. 4. %OS = 16.3 %
  5. 5. %OS = 74.13 %
  6. 6. ωn = 21.7 rad/s

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