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)y(∞) = ?

A first-order system G(s) = 10/(4s + 1) receives a step input of size 1 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 10/(4s + 1)U = 1
y(∞) =
2.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 50/(s + 10) receives a step input of size 20 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 50/(s + 10)U = 20
y(∞) =
3.Medium
t (s)y(t)2

A system has the transfer function G(s) = 136/(s² + 13s + 68) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 136/(s² + 13s + 68)
σ =
4.Medium
t (s)y(t)3ts​ = ?

A system has the transfer function G(s) = 186/(s² + 5s + 62) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 186/(s² + 5s + 62)
ts = s
5.Hard
k = 1000 N/mc = 27 N·s/mm = 2 kgF = 20 Nx(t)

A mass m = 2 kg hangs on a spring k = 1000 N/m with a viscous damper c = 27 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 percent overshoot %OS of the displacement.

m = 2 kgk = 1000 N/mc = 27 N·s/mF = 20 N
%OS = %
6.Hard
R(s)+Ks(s + 20)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 20)). Find the gain K that gives a step response with 2 % overshoot.

G(s) = K/(s(s + 20))%OS = 2 %
K =

Answer key

  1. 1. y(∞) = 10
  2. 2. y(∞) = 100
  3. 3. σ = −6.5
  4. 4. ts = 1.6 s
  5. 5. %OS = 36.98 %
  6. 6. K = 164.5

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