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 = 2.2 kΩC = 47 µFvC​

An uncharged capacitor C = 47 µF is charged from a 24 V step source through a resistor R = 2.2 kΩ. Find the 10–90 % rise time tr of the capacitor voltage, in ms.

R = 2.2 kΩC = 47 µFV = 24 V
tr = ms
2.Easy
t (s)y(t)1001.5 s?

A first-order system G(s) = 10/(0.5s + 1) receives a step input of size 10 at t = 0, starting from rest. Find the output y(1.5) at t = 1.5 s.

G(s) = 10/(0.5s + 1)U = 10t = 1.5 s
y(1.5) =
3.Medium
t (s)y(t)3tp​ = ?

A system has the transfer function G(s) = 195/(s² + 6s + 65) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 195/(s² + 6s + 65)
tp = s
4.Medium
t (s)y(t)3

A system has the transfer function G(s) = 120/(s² + 5s + 40) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 120/(s² + 5s + 40)
σ =
5.Hard
R(s)+285s(s + 16)G(s)C(s)−

A unity negative feedback loop has G(s) = 285/(s(s + 16)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 285/(s(s + 16))
ts = s
6.Hard
+−12 VR = 28 ΩL = 50 mHC = 10 µFvC​

A series RLC circuit with R = 28 Ω, L = 50 mH and C = 10 µF is connected to a 12 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the peak capacitor voltage vC,max.

R = 28 ΩL = 50 mHC = 10 µFV = 12 V
vC,max = V

Answer key

  1. 1. tr = 227.2 ms
  2. 2. y(1.5) = 95.02
  3. 3. tp = 0.4198 s
  4. 4. σ = −2.5
  5. 5. ts = 0.5 s
  6. 6. vC,max = 18.36 V

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