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)10.25 s?

A first-order system G(s) = 2/(s + 4) receives a step input of size 2 at t = 0, starting from rest. Find the output y(0.25) at t = 0.25 s.

G(s) = 2/(s + 4)U = 2t = 0.25 s
y(0.25) =
2.Easy
t (s)y(t)4t = ?80 %

A first-order system G(s) = 4/(s + 2) receives a step input of size 2 at t = 0, starting from rest. How long does the output take to reach 80 % of its final value? Find t.

G(s) = 4/(s + 2)U = 280 %
t = s
3.Medium
t (s)y(t)1ts​ = ?

A system has the transfer function G(s) = 47/(s² + 5s + 47) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 47/(s² + 5s + 47)
ts = s
4.Medium
t (s)y(t)3ts​ = ?

A system has the transfer function G(s) = 234/(s² + 4s + 78) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 234/(s² + 4s + 78)
ts = s
5.Hard
k = 5000 N/mc = 190 N·s/mm = 5 kgF = 100 Nx(t)

A mass m = 5 kg hangs on a spring k = 5000 N/m with a viscous damper c = 190 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 damping ratio ζ.

m = 5 kgk = 5000 N/mc = 190 N·s/mF = 100 N
ζ =
6.Hard
R(s)+Ks(s + 5)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 5)). Find the gain K that gives a step response with 10 % overshoot.

G(s) = K/(s(s + 5))%OS = 10 %
K =

Answer key

  1. 1. y(0.25) = 0.6321
  2. 2. t = 0.8047 s
  3. 3. ts = 1.6 s
  4. 4. ts = 2 s
  5. 5. ζ = 0.6008
  6. 6. K = 17.88

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