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 = 47 kΩC = 47 µFvC​

An uncharged capacitor C = 47 µF is charged from a 5 V step source through a resistor R = 47 kΩ. Find the 10–90 % rise time tr of the capacitor voltage, in ms.

R = 47 kΩC = 47 µFV = 5 V
tr = ms
2.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 2.5/(4s + 1) receives a step input of size 10 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 2.5/(4s + 1)U = 10
y(∞) =
3.Medium
t (s)y(t)3ts​ = ?

A system has the transfer function G(s) = 168/(s² + 2s + 56) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 168/(s² + 2s + 56)
ts = s
4.Medium
t (s)y(t)1ts​ = ?

A system has the transfer function G(s) = 79/(s² + 4s + 79) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 79/(s² + 4s + 79)
ts = s
5.Hard
t (s)y(t)15 %

A second-order system without zeros must have a step response with 5 % overshoot. Find the damping ratio ζ.

%OS = 5 %
ζ =
6.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 25 % overshoot.

G(s) = K/(s(s + 12))%OS = 25 %
K =

Answer key

  1. 1. tr = 4854 ms
  2. 2. y(∞) = 25
  3. 3. ts = 4 s
  4. 4. ts = 2 s
  5. 5. ζ = 0.6901
  6. 6. K = 220.9

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