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
+−5 VR = 10 kΩC = 1 µFvC​

An uncharged capacitor C = 1 µF is charged from a 5 V step source through a resistor R = 10 kΩ. Find the capacitor voltage vC at t = 7 ms.

R = 10 kΩC = 1 µFV = 5 Vt = 7 ms
vC = V
2.Easy
t (s)y(t)501 s?

A first-order system G(s) = 2.5/(2s + 1) receives a step input of size 20 at t = 0, starting from rest. Find the output y(1) at t = 1 s.

G(s) = 2.5/(2s + 1)U = 20t = 1 s
y(1) =
3.Medium
t (s)y(t)1ts​ = ?

A system has the transfer function G(s) = 49/(s² + 8s + 49) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 49/(s² + 8s + 49)
ts = s
4.Medium
t (s)y(t)2ts​ = ?

A system has the transfer function G(s) = 120/(s² + 9s + 60) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 120/(s² + 9s + 60)
ts = s
5.Hard
R(s)+Ks(s + 12)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 12)). Find the gain K that gives a step response with 15 % overshoot.

G(s) = K/(s(s + 12))%OS = 15 %
K =
6.Hard
t (s)y(t)112 %

A second-order system without zeros must have a step response with 12 % overshoot. Find the damping ratio ζ.

%OS = 12 %
ζ =

Answer key

  1. 1. vC = 2.517 V
  2. 2. y(1) = 19.67
  3. 3. ts = 1 s
  4. 4. ts = 0.8889 s
  5. 5. K = 134.7
  6. 6. ζ = 0.5594

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