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
+−12 VR = 1 kΩC = 1 µFvC​

An uncharged capacitor C = 1 µF is charged from a 12 V step source through a resistor R = 1 kΩ. How long after closing the switch does the capacitor voltage reach 99 % of its final value? Find t in ms.

R = 1 kΩC = 1 µFV = 12 V99 %
t = ms
2.Easy
t (s)y(t)50t = ?95 %

A first-order system G(s) = 10/(s + 2) receives a step input of size 10 at t = 0, starting from rest. How long does the output take to reach 95 % of its final value? Find t.

G(s) = 10/(s + 2)U = 1095 %
t = s
3.Medium
t (s)y(t)0.5

A system has the transfer function G(s) = 15.5/(s² + 4s + 31) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 15.5/(s² + 4s + 31)
σ =
4.Medium
t (s)y(t)2?

A system has the transfer function G(s) = 86/(s² + 6s + 43) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 86/(s² + 6s + 43)
%OS = %
5.Hard
R(s)+70s(s + 2)G(s)C(s)−

A unity negative feedback loop has G(s) = 70/(s(s + 2)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 70/(s(s + 2))
ts = s
6.Hard
t (s)y(t)12 %

A second-order system without zeros must have a step response with 2 % overshoot. Find the damping ratio ζ.

%OS = 2 %
ζ =

Answer key

  1. 1. t = 4.605 ms
  2. 2. t = 1.498 s
  3. 3. σ = −2
  4. 4. %OS = 19.86 %
  5. 5. ts = 4 s
  6. 6. ζ = 0.7797

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