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)52 s?

A first-order system G(s) = 0.5/(10s + 1) receives a step input of size 10 at t = 0, starting from rest. Find the output y(2) at t = 2 s.

G(s) = 0.5/(10s + 1)U = 10t = 2 s
y(2) =
2.Easy
t (s)y(t)503 s25

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 50. At t = 3 s it reads 25. Find the time constant τ.

y(∞) = 50y(3) = 25
τ = s
3.Medium
t (s)y(t)1?

A system has the transfer function G(s) = 51/(s² + 2s + 51) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 51/(s² + 2s + 51)
%OS = %
4.Medium
t (s)y(t)0.5tp​ = ?

A system has the transfer function G(s) = 32/(s² + 3s + 64) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 32/(s² + 3s + 64)
tp = s
5.Hard
+−10 VR = 18 ΩL = 20 mHC = 10 µFvC​

A series RLC circuit with R = 18 Ω, L = 20 mH and C = 10 µF is connected to a 10 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the time tp of the first voltage peak, in ms.

R = 18 ΩL = 20 mHC = 10 µFV = 10 V
tp = ms
6.Hard
t (s)y(t)1tp​ = 0.8 s40 %

The step response of a second-order system without zeros shows 40 % overshoot, and the first peak occurs at t = 0.8 s. Find the natural frequency ωn.

%OS = 40 %tp = 0.8 s
ωn = rad/s

Answer key

  1. 1. y(2) = 0.9063
  2. 2. τ = 4.328 s
  3. 3. %OS = 64.13 %
  4. 4. tp = 0.3998 s
  5. 5. tp = 1.434 ms
  6. 6. ωn = 4.091 rad/s

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