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
+−24 VR = 22 kΩC = 22 µFvC​

An uncharged capacitor C = 22 µF is charged from a 24 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 = 22 µFV = 24 V
tr = ms
2.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 4/(0.8s + 1) receives a step input of size 5 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 4/(0.8s + 1)U = 5
y(∞) =
3.Medium
t (s)y(t)1ts​ = ?

A system has the transfer function G(s) = 49/(s² + 3s + 49) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 49/(s² + 3s + 49)
ts = s
4.Medium
t (s)y(t)2?

A system has the transfer function G(s) = 62/(s² + 2s + 31) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 62/(s² + 2s + 31)
%OS = %
5.Hard
R(s)+Ks(s + 12)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 12)). Find the gain K that gives a step response with 25 % overshoot.

G(s) = K/(s(s + 12))%OS = 25 %
K =
6.Hard
k = 2000 N/mc = 89 N·s/mm = 4 kgF = 20 Nx(t)

A mass m = 4 kg hangs on a spring k = 2000 N/m with a viscous damper c = 89 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 damping ratio ζ.

m = 4 kgk = 2000 N/mc = 89 N·s/mF = 20 N
ζ =

Answer key

  1. 1. tr = 1063 ms
  2. 2. y(∞) = 20
  3. 3. ts = 2.667 s
  4. 4. %OS = 56.35 %
  5. 5. K = 220.9
  6. 6. ζ = 0.4975

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