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
t (s)y(t)50t = ?75 %

A first-order system G(s) = 10/(2s + 1) receives a step input of size 5 at t = 0, starting from rest. How long does the output take to reach 75 % of its final value? Find t.

G(s) = 10/(2s + 1)U = 575 %
t = s
2.Easy
+−10 VR = 10 kΩC = 22 µFvC​

An uncharged capacitor C = 22 µF is charged from a 10 V step source through a resistor R = 10 kΩ. How long after closing the switch does the capacitor voltage reach 95 % of its final value? Find t in ms.

R = 10 kΩC = 22 µFV = 10 V95 %
t = ms
3.Medium
t (s)y(t)1

A system has the transfer function G(s) = 33/(s² + 4s + 33) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 33/(s² + 4s + 33)
σ =
4.Medium
t (s)y(t)1

A system has the transfer function G(s) = 12/(s² + 2s + 12) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 12/(s² + 2s + 12)
σ =
5.Hard
R(s)+45s(s + 8)G(s)C(s)−

A unity negative feedback loop has G(s) = 45/(s(s + 8)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 45/(s(s + 8))
ts = s
6.Hard
+−10 VR = 4 ΩL = 10 mHC = 100 µFvC​

A series RLC circuit with R = 4 Ω, L = 10 mH and C = 100 µF is connected to a 10 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the time tp of the first voltage peak, in ms.

R = 4 ΩL = 10 mHC = 100 µFV = 10 V
tp = ms

Answer key

  1. 1. t = 2.773 s
  2. 2. t = 659.1 ms
  3. 3. σ = −2
  4. 4. σ = −1
  5. 5. ts = 1 s
  6. 6. tp = 3.206 ms

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