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 90 % of its final value? Find t in ms.

R = 1 kΩC = 1 µFV = 12 V90 %
t = ms
2.Easy
t (s)y(t)2010 s18

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 20. At t = 10 s it reads 18. Find the time constant τ.

y(∞) = 20y(10) = 18
τ = s
3.Medium
t (s)y(t)2

A system has the transfer function G(s) = 58/(s² + 3s + 29) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 58/(s² + 3s + 29)
σ =
4.Medium
t (s)y(t)1?

A system has the transfer function G(s) = 29/(s² + 4s + 29) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 29/(s² + 4s + 29)
%OS = %
5.Hard
R(s)+55s(s + 5)G(s)C(s)−

A unity negative feedback loop has G(s) = 55/(s(s + 5)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 55/(s(s + 5))
ts = s
6.Hard
t (s)y(t)120 %

A second-order system without zeros must have a step response with 20 % overshoot. Find the damping ratio ζ.

%OS = 20 %
ζ =

Answer key

  1. 1. t = 2.303 ms
  2. 2. τ = 4.343 s
  3. 3. σ = −1.5
  4. 4. %OS = 28.46 %
  5. 5. ts = 1.6 s
  6. 6. ζ = 0.4559

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