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
+−10 VR = 1 kΩC = 10 µFvC​

An uncharged capacitor C = 10 µF is charged from a 10 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 = 10 µFV = 10 V90 %
t = ms
2.Easy
t (s)y(t)40t = ?50 %

A first-order system G(s) = 2/(s + 1) receives a step input of size 20 at t = 0, starting from rest. How long does the output take to reach 50 % of its final value? Find t.

G(s) = 2/(s + 1)U = 2050 %
t = s
3.Medium
t (s)y(t)0.5

A system has the transfer function G(s) = 18/(s² + 2s + 36) and receives a unit step input. Find the natural frequency ωn in rad/s.

G(s) = 18/(s² + 2s + 36)
ωn = rad/s
4.Medium
t (s)y(t)2ts​ = ?

A system has the transfer function G(s) = 84/(s² + 4s + 42) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 84/(s² + 4s + 42)
ts = s
5.Hard
R(s)+65s(s + 8)G(s)C(s)−

A unity negative feedback loop has G(s) = 65/(s(s + 8)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 65/(s(s + 8))
ts = s
6.Hard
R(s)+Ks(s + 20)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 20)). Find the gain K that gives a step response with 30 % overshoot.

G(s) = K/(s(s + 20))%OS = 30 %
K =

Answer key

  1. 1. t = 23.03 ms
  2. 2. t = 0.6931 s
  3. 3. ωn = 6 rad/s
  4. 4. ts = 2 s
  5. 5. ts = 1 s
  6. 6. K = 780.9

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