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

G(s) = 10/(s + 5)U = 5
y(∞) =
2.Easy
+−10 VR = 22 kΩC = 1 µFvC​

An uncharged capacitor C = 1 µF is charged from a 10 V step source through a resistor R = 22 kΩ. Find the 10–90 % rise time tr of the capacitor voltage, in ms.

R = 22 kΩC = 1 µFV = 10 V
tr = ms
3.Medium
t (s)y(t)1tp​ = ?

A system has the transfer function G(s) = 85/(s² + 6s + 85) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 85/(s² + 6s + 85)
tp = s
4.Medium
t (s)y(t)1?

A system has the transfer function G(s) = 39/(s² + 7s + 39) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 39/(s² + 7s + 39)
%OS = %
5.Hard
R(s)+Ks(s + 8)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 8)). Find the gain K that gives a step response with 30 % overshoot.

G(s) = K/(s(s + 8))%OS = 30 %
K =
6.Hard
k = 100 N/mc = 24 N·s/mm = 4 kgF = 50 Nx(t)

A mass m = 4 kg hangs on a spring k = 100 N/m with a viscous damper c = 24 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 damping ratio ζ.

m = 4 kgk = 100 N/mc = 24 N·s/mF = 50 N
ζ =

Answer key

  1. 1. y(∞) = 10
  2. 2. tr = 48.34 ms
  3. 3. tp = 0.3604 s
  4. 4. %OS = 11.93 %
  5. 5. K = 124.9
  6. 6. ζ = 0.6

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