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)510 s2

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 5. At t = 10 s it reads 2. Find the time constant τ.

y(∞) = 5y(10) = 2
τ = s
2.Easy
t (s)y(t)251.4 s?

A first-order system G(s) = 2.5/(s + 0.5) receives a step input of size 5 at t = 0, starting from rest. Find the output y(1.4) at t = 1.4 s.

G(s) = 2.5/(s + 0.5)U = 5t = 1.4 s
y(1.4) =
3.Medium
t (s)y(t)1tp​ = ?

A system has the transfer function G(s) = 61/(s² + 3s + 61) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 61/(s² + 3s + 61)
tp = s
4.Medium
t (s)y(t)2

A system has the transfer function G(s) = 120/(s² + 7s + 60) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 120/(s² + 7s + 60)
σ =
5.Hard
+−5 VR = 63 ΩL = 100 mHC = 1 µFvC​

A series RLC circuit with R = 63 Ω, L = 100 mH and C = 1 µF is connected to a 5 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 = 63 ΩL = 100 mHC = 1 µFV = 5 V
ωn = rad/s
6.Hard
R(s)+150s(s + 16)G(s)C(s)−

A unity negative feedback loop has G(s) = 150/(s(s + 16)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 150/(s(s + 16))
ts = s

Answer key

  1. 1. τ = 19.58 s
  2. 2. y(1.4) = 12.59
  3. 3. tp = 0.4099 s
  4. 4. σ = −3.5
  5. 5. ωn = 3162 rad/s
  6. 6. ts = 0.5 s

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