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)y(∞) = ?

A first-order system G(s) = 2.5/(5s + 1) receives a step input of size 1 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 2.5/(5s + 1)U = 1
y(∞) =
2.Easy
+−9 VR = 47 kΩC = 1 µFvC​

An uncharged capacitor C = 1 µF is charged from a 9 V step source through a resistor R = 47 kΩ. Find the capacitor voltage vC at t = 32.9 ms.

R = 47 kΩC = 1 µFV = 9 Vt = 32.9 ms
vC = V
3.Medium
t (s)y(t)3?

A system has the transfer function G(s) = 117/(s² + 9s + 39) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 117/(s² + 9s + 39)
%OS = %
4.Medium
t (s)y(t)0.5?

A system has the transfer function G(s) = 34/(s² + 11s + 68) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 34/(s² + 11s + 68)
%OS = %
5.Hard
R(s)+Ks(s + 2)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 2)). Find the gain K that gives a step response with 10 % overshoot.

G(s) = K/(s(s + 2))%OS = 10 %
K =
6.Hard
t (s)y(t)1tp​ = 0.5 s5 %

The step response of a second-order system without zeros shows 5 % overshoot, and the first peak occurs at t = 0.5 s. Find the natural frequency ωn.

%OS = 5 %tp = 0.5 s
ωn = rad/s

Answer key

  1. 1. y(∞) = 2.5
  2. 2. vC = 4.531 V
  3. 3. %OS = 3.82 %
  4. 4. %OS = 6.007 %
  5. 5. K = 2.862
  6. 6. ωn = 8.682 rad/s

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