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
+−5 VR = 47 kΩC = 4.7 µFvC​

An uncharged capacitor C = 4.7 µF is charged from a 5 V step source through a resistor R = 47 kΩ. Find the capacitor voltage vC at t = 220.9 ms.

R = 47 kΩC = 4.7 µFV = 5 Vt = 220.9 ms
vC = V
2.Easy
t (s)y(t)20t = ?90 %

A first-order system G(s) = 10/(0.8s + 1) receives a step input of size 2 at t = 0, starting from rest. How long does the output take to reach 90 % of its final value? Find t.

G(s) = 10/(0.8s + 1)U = 290 %
t = s
3.Medium
t (s)y(t)2ts​ = ?

A system has the transfer function G(s) = 24/(s² + 2s + 12) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 24/(s² + 2s + 12)
ts = s
4.Medium
t (s)y(t)2

A system has the transfer function G(s) = 124/(s² + 6s + 62) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 124/(s² + 6s + 62)
σ =
5.Hard
R(s)+245s(s + 5)G(s)C(s)−

A unity negative feedback loop has G(s) = 245/(s(s + 5)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 245/(s(s + 5))
ts = s
6.Hard
+−10 VR = 126 ΩL = 50 mHC = 2 µFvC​

A series RLC circuit with R = 126 Ω, L = 50 mH and C = 2 µF is connected to a 10 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the percent overshoot %OS of the capacitor voltage.

R = 126 ΩL = 50 mHC = 2 µFV = 10 V
%OS = %

Answer key

  1. 1. vC = 3.161 V
  2. 2. t = 1.842 s
  3. 3. ts = 4 s
  4. 4. σ = −3
  5. 5. ts = 1.6 s
  6. 6. %OS = 25.54 %

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