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)22 s?

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

G(s) = 1/(2s + 1)U = 2t = 2 s
y(2) =
2.Easy
+−12 VR = 2.2 kΩC = 22 µFvC​

An uncharged capacitor C = 22 µF is charged from a 12 V step source through a resistor R = 2.2 kΩ. How long after closing the switch does the capacitor voltage reach 50 % of its final value? Find t in ms.

R = 2.2 kΩC = 22 µFV = 12 V50 %
t = ms
3.Medium
t (s)y(t)1ts​ = ?

A system has the transfer function G(s) = 80/(s² + 5s + 80) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 80/(s² + 5s + 80)
ts = s
4.Medium
t (s)y(t)1

A system has the transfer function G(s) = 31/(s² + 8s + 31) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 31/(s² + 8s + 31)
σ =
5.Hard
R(s)+Ks(s + 6)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 6)). Find the gain K that gives a step response with 30 % overshoot.

G(s) = K/(s(s + 6))%OS = 30 %
K =
6.Hard
+−10 VR = 21 ΩL = 50 mHC = 4.7 µFvC​

A series RLC circuit with R = 21 Ω, L = 50 mH and C = 4.7 µF is connected to a 10 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 = 21 ΩL = 50 mHC = 4.7 µFV = 10 V
ωn = rad/s

Answer key

  1. 1. y(2) = 1.264
  2. 2. t = 33.55 ms
  3. 3. ts = 1.6 s
  4. 4. σ = −4
  5. 5. K = 70.28
  6. 6. ωn = 2063 rad/s

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