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 = 100 kΩC = 100 µFvC​

An uncharged capacitor C = 100 µF is charged from a 5 V step source through a resistor R = 100 kΩ. Find the 10–90 % rise time tr of the capacitor voltage, in ms.

R = 100 kΩC = 100 µFV = 5 V
tr = ms
2.Easy
t (s)y(t)5t = ?50 %

A first-order system G(s) = 1/(5s + 1) receives a step input of size 5 at t = 0, starting from rest. How long does the output take to reach 50 % of its final value? Find t.

G(s) = 1/(5s + 1)U = 550 %
t = s
3.Medium
t (s)y(t)1

A system has the transfer function G(s) = 62/(s² + 5s + 62) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 62/(s² + 5s + 62)
σ =
4.Medium
t (s)y(t)1

A system has the transfer function G(s) = 85/(s² + 9s + 85) and receives a unit step input. Find the damping ratio ζ.

G(s) = 85/(s² + 9s + 85)
ζ =
5.Hard
t (s)y(t)1tp​ = 0.8 s30 %

The step response of a second-order system without zeros shows 30 % overshoot, and the first peak occurs at t = 0.8 s. Find the natural frequency ωn.

%OS = 30 %tp = 0.8 s
ωn = rad/s
6.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 =

Answer key

  1. 1. tr = 21972 ms
  2. 2. t = 3.466 s
  3. 3. σ = −2.5
  4. 4. ζ = 0.4881
  5. 5. ωn = 4.205 rad/s
  6. 6. ζ = 0.4037

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