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
+−9 VR = 10 kΩC = 1 µFvC​

An uncharged capacitor C = 1 µF is charged from a 9 V step source through a resistor R = 10 kΩ. Find the capacitor voltage vC at t = 7 ms.

R = 10 kΩC = 1 µFV = 9 Vt = 7 ms
vC = V
2.Easy
+−9 VR = 2.2 kΩC = 22 µFvC​

An uncharged capacitor C = 22 µF is charged from a 9 V step source through a resistor R = 2.2 kΩ. Find the capacitor voltage vC at t = 12.1 ms.

R = 2.2 kΩC = 22 µFV = 9 Vt = 12.1 ms
vC = V
3.Medium
t (s)y(t)1

A system has the transfer function G(s) = 38/(s² + 8s + 38) and receives a unit step input. Find the damping ratio ζ.

G(s) = 38/(s² + 8s + 38)
ζ =
4.Medium
t (s)y(t)2?

A system has the transfer function G(s) = 158/(s² + 13s + 79) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 158/(s² + 13s + 79)
%OS = %
5.Hard
+−10 VR = 40 ΩL = 20 mHC = 2 µFvC​

A series RLC circuit with R = 40 Ω, L = 20 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 = 40 ΩL = 20 mHC = 2 µFV = 10 V
%OS = %
6.Hard
R(s)+160s(s + 8)G(s)C(s)−

A unity negative feedback loop has G(s) = 160/(s(s + 8)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 160/(s(s + 8))
ts = s

Answer key

  1. 1. vC = 4.531 V
  2. 2. vC = 1.991 V
  3. 3. ζ = 0.6489
  4. 4. %OS = 3.444 %
  5. 5. %OS = 52.66 %
  6. 6. ts = 1 s

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