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)y(∞) = ?

A first-order system G(s) = 4/(1s + 1) receives a step input of size 2 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 4/(1s + 1)U = 2
y(∞) =
2.Easy
t (s)y(t)103 s?

A first-order system G(s) = 10/(2s + 1) receives a step input of size 1 at t = 0, starting from rest. Find the output y(3) at t = 3 s.

G(s) = 10/(2s + 1)U = 1t = 3 s
y(3) =
3.Medium
t (s)y(t)1

A system has the transfer function G(s) = 21/(s² + 6s + 21) and receives a unit step input. Find the damping ratio ζ.

G(s) = 21/(s² + 6s + 21)
ζ =
4.Medium
t (s)y(t)3

A system has the transfer function G(s) = 165/(s² + 2s + 55) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 165/(s² + 2s + 55)
σ =
5.Hard
+−12 VR = 39 ΩL = 50 mHC = 47 µFvC​

A series RLC circuit with R = 39 Ω, L = 50 mH and C = 47 µF is connected to a 12 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the undamped natural frequency ωn in rad/s.

R = 39 ΩL = 50 mHC = 47 µFV = 12 V
ωn = rad/s
6.Hard
+−5 VR = 849 ΩL = 500 mHC = 1 µFvC​

A series RLC circuit with R = 849 Ω, L = 500 mH and C = 1 µF is connected to a 5 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 = 849 ΩL = 500 mHC = 1 µFV = 5 V
%OS = %

Answer key

  1. 1. y(∞) = 8
  2. 2. y(3) = 7.769
  3. 3. ζ = 0.6547
  4. 4. σ = −1
  5. 5. ωn = 652.3 rad/s
  6. 6. %OS = 9.459 %

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