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
+−10 VR = 1 kΩC = 22 µFvC​

An uncharged capacitor C = 22 µF is charged from a 10 V step source through a resistor R = 1 kΩ. Find the 10–90 % rise time tr of the capacitor voltage, in ms.

R = 1 kΩC = 22 µFV = 10 V
tr = ms
2.Easy
t (s)y(t)500.3 s?

A first-order system G(s) = 25/(s + 5) receives a step input of size 10 at t = 0, starting from rest. Find the output y(0.3) at t = 0.3 s.

G(s) = 25/(s + 5)U = 10t = 0.3 s
y(0.3) =
3.Medium
t (s)y(t)3tp​ = ?

A system has the transfer function G(s) = 243/(s² + 12s + 81) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 243/(s² + 12s + 81)
tp = s
4.Medium
t (s)y(t)3

A system has the transfer function G(s) = 96/(s² + 6s + 32) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 96/(s² + 6s + 32)
σ =
5.Hard
t (s)y(t)125 %

A second-order system without zeros must have a step response with 25 % overshoot. Find the damping ratio ζ.

%OS = 25 %
ζ =
6.Hard
+−12 VR = 52 ΩL = 200 mHC = 47 µFvC​

A series RLC circuit with R = 52 Ω, L = 200 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 = 52 ΩL = 200 mHC = 47 µFV = 12 V
ωn = rad/s

Answer key

  1. 1. tr = 48.34 ms
  2. 2. y(0.3) = 38.84
  3. 3. tp = 0.4683 s
  4. 4. σ = −3
  5. 5. ζ = 0.4037
  6. 6. ωn = 326.2 rad/s

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