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)1t = ?60 %

A first-order system G(s) = 2/(s + 4) receives a step input of size 2 at t = 0, starting from rest. How long does the output take to reach 60 % of its final value? Find t.

G(s) = 2/(s + 4)U = 260 %
t = s
2.Easy
t (s)y(t)0.50.14 s?

A first-order system G(s) = 2.5/(s + 5) receives a step input of size 1 at t = 0, starting from rest. Find the output y(0.14) at t = 0.14 s.

G(s) = 2.5/(s + 5)U = 1t = 0.14 s
y(0.14) =
3.Medium
t (s)y(t)2ts​ = ?

A system has the transfer function G(s) = 20/(s² + 4s + 10) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 20/(s² + 4s + 10)
ts = s
4.Medium
t (s)y(t)2

A system has the transfer function G(s) = 28/(s² + s + 14) and receives a unit step input. Find the damping ratio ζ.

G(s) = 28/(s² + s + 14)
ζ =
5.Hard
k = 5000 N/mc = 20 N·s/mm = 2 kgF = 50 Nx(t)

A mass m = 2 kg hangs on a spring k = 5000 N/m with a viscous damper c = 20 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 time tp at which the displacement is largest.

m = 2 kgk = 5000 N/mc = 20 N·s/mF = 50 N
tp = s
6.Hard
R(s)+105s(s + 16)G(s)C(s)−

A unity negative feedback loop has G(s) = 105/(s(s + 16)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 105/(s(s + 16))
ts = s

Answer key

  1. 1. t = 0.2291 s
  2. 2. y(0.14) = 0.2517
  3. 3. ts = 2 s
  4. 4. ζ = 0.1336
  5. 5. tp = 0.06315 s
  6. 6. ts = 0.5 s

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