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 = 4.7 kΩC = 10 µFvC​

An uncharged capacitor C = 10 µF is charged from a 5 V step source through a resistor R = 4.7 kΩ. Find the capacitor voltage vC at t = 94 ms.

R = 4.7 kΩC = 10 µFV = 5 Vt = 94 ms
vC = V
2.Easy
+−9 VR = 10 kΩC = 22 µFvC​

An uncharged capacitor C = 22 µF is charged from a 9 V step source through a resistor R = 10 kΩ. Find the 10–90 % rise time tr of the capacitor voltage, in ms.

R = 10 kΩC = 22 µFV = 9 V
tr = ms
3.Medium
t (s)y(t)0.5tp​ = ?

A system has the transfer function G(s) = 37.5/(s² + 10s + 75) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 37.5/(s² + 10s + 75)
tp = s
4.Medium
t (s)y(t)2

A system has the transfer function G(s) = 82/(s² + 9s + 41) and receives a unit step input. Find the damping ratio ζ.

G(s) = 82/(s² + 9s + 41)
ζ =
5.Hard
k = 800 N/mc = 54 N·s/mm = 2.5 kgF = 20 Nx(t)

A mass m = 2.5 kg hangs on a spring k = 800 N/m with a viscous damper c = 54 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 = 2.5 kgk = 800 N/mc = 54 N·s/mF = 20 N
%OS = %
6.Hard
R(s)+80s(s + 2)G(s)C(s)−

A unity negative feedback loop has G(s) = 80/(s(s + 2)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 80/(s(s + 2))
ts = s

Answer key

  1. 1. vC = 4.323 V
  2. 2. tr = 483.4 ms
  3. 3. tp = 0.4443 s
  4. 4. ζ = 0.7028
  5. 5. %OS = 9.262 %
  6. 6. ts = 4 s

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