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) = 40/(s + 20) receives a step input of size 1 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 40/(s + 20)U = 1
y(∞) =
2.Easy
+−24 VR = 2.2 kΩC = 47 µFvC​

An uncharged capacitor C = 47 µF is charged from a 24 V step source through a resistor R = 2.2 kΩ. Find the 10–90 % rise time tr of the capacitor voltage, in ms.

R = 2.2 kΩC = 47 µFV = 24 V
tr = ms
3.Medium
t (s)y(t)2tp​ = ?

A system has the transfer function G(s) = 42/(s² + 5s + 21) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 42/(s² + 5s + 21)
tp = s
4.Medium
t (s)y(t)1?

A system has the transfer function G(s) = 12/(s² + 4s + 12) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 12/(s² + 4s + 12)
%OS = %
5.Hard
t (s)y(t)1tp​ = 1 s5 %

The step response of a second-order system without zeros shows 5 % overshoot, and the first peak occurs at t = 1 s. Find the natural frequency ωn.

%OS = 5 %tp = 1 s
ωn = rad/s
6.Hard
t (s)y(t)1tp​ = 0.5 s10 %

The step response of a second-order system without zeros shows 10 % overshoot, and the first peak occurs at t = 0.5 s. Find the natural frequency ωn.

%OS = 10 %tp = 0.5 s
ωn = rad/s

Answer key

  1. 1. y(∞) = 2
  2. 2. tr = 227.2 ms
  3. 3. tp = 0.818 s
  4. 4. %OS = 10.85 %
  5. 5. ωn = 4.341 rad/s
  6. 6. ωn = 7.79 rad/s

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