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
+−24 VR = 100 kΩC = 1 µFvC​

An uncharged capacitor C = 1 µF is charged from a 24 V step source through a resistor R = 100 kΩ. Find the 10–90 % rise time tr of the capacitor voltage, in ms.

R = 100 kΩC = 1 µFV = 24 V
tr = ms
2.Easy
t (s)y(t)25t = ?95 %

A first-order system G(s) = 50/(s + 10) receives a step input of size 5 at t = 0, starting from rest. How long does the output take to reach 95 % of its final value? Find t.

G(s) = 50/(s + 10)U = 595 %
t = s
3.Medium
t (s)y(t)1

A system has the transfer function G(s) = 72/(s² + 3s + 72) and receives a unit step input. Find the natural frequency ωn in rad/s.

G(s) = 72/(s² + 3s + 72)
ωn = rad/s
4.Medium
t (s)y(t)1tp​ = ?

A system has the transfer function G(s) = 86/(s² + 14s + 86) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 86/(s² + 14s + 86)
tp = s
5.Hard
R(s)+Ks(s + 4)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 4)). Find the gain K that gives a step response with 15 % overshoot.

G(s) = K/(s(s + 4))%OS = 15 %
K =
6.Hard
t (s)y(t)1tp​ = 1 s4.3 %

The step response of a second-order system without zeros shows 4.3 % overshoot, and the first peak occurs at t = 1 s. Find the natural frequency ωn.

%OS = 4.3 %tp = 1 s
ωn = rad/s

Answer key

  1. 1. tr = 219.7 ms
  2. 2. t = 0.2996 s
  3. 3. ωn = 8.485 rad/s
  4. 4. tp = 0.5165 s
  5. 5. K = 14.97
  6. 6. ωn = 4.446 rad/s

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