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)50t = ?98 %

A first-order system G(s) = 5/(0.8s + 1) receives a step input of size 10 at t = 0, starting from rest. How long does the output take to reach 98 % of its final value? Find t.

G(s) = 5/(0.8s + 1)U = 1098 %
t = s
2.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 20/(s + 20) receives a step input of size 5 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 20/(s + 20)U = 5
y(∞) =
3.Medium
t (s)y(t)0.5

A system has the transfer function G(s) = 33/(s² + 8s + 66) and receives a unit step input. Find the damping ratio ζ.

G(s) = 33/(s² + 8s + 66)
ζ =
4.Medium
t (s)y(t)3

A system has the transfer function G(s) = 15/(s² + s + 5) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 15/(s² + s + 5)
σ =
5.Hard
t (s)y(t)18 %

A second-order system without zeros must have a step response with 8 % overshoot. Find the damping ratio ζ.

%OS = 8 %
ζ =
6.Hard
k = 2000 N/mc = 38 N·s/mm = 8 kgF = 20 Nx(t)

A mass m = 8 kg hangs on a spring k = 2000 N/m with a viscous damper c = 38 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 20 N is suddenly applied. Find the time tp at which the displacement is largest.

m = 8 kgk = 2000 N/mc = 38 N·s/mF = 20 N
tp = s

Answer key

  1. 1. t = 3.13 s
  2. 2. y(∞) = 5
  3. 3. ζ = 0.4924
  4. 4. σ = −0.5
  5. 5. ζ = 0.6266
  6. 6. tp = 0.201 s

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