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 = 100 kΩC = 4.7 µFvC​

An uncharged capacitor C = 4.7 µF is charged from a 5 V step source through a resistor R = 100 kΩ. Find the capacitor voltage vC at t = 705 ms.

R = 100 kΩC = 4.7 µFV = 5 Vt = 705 ms
vC = V
2.Easy
t (s)y(t)401 s?

A first-order system G(s) = 1/(s + 0.5) receives a step input of size 20 at t = 0, starting from rest. Find the output y(1) at t = 1 s.

G(s) = 1/(s + 0.5)U = 20t = 1 s
y(1) =
3.Medium
t (s)y(t)1tp​ = ?

A system has the transfer function G(s) = 27/(s² + 6s + 27) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 27/(s² + 6s + 27)
tp = s
4.Medium
t (s)y(t)0.5

A system has the transfer function G(s) = 39/(s² + 4s + 78) and receives a unit step input. Find the natural frequency ωn in rad/s.

G(s) = 39/(s² + 4s + 78)
ωn = rad/s
5.Hard
+−12 VR = 38 ΩL = 50 mHC = 22 µFvC​

A series RLC circuit with R = 38 Ω, L = 50 mH and C = 22 µF is connected to a 12 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the time tp of the first voltage peak, in ms.

R = 38 ΩL = 50 mHC = 22 µFV = 12 V
tp = ms
6.Hard
t (s)y(t)110 %

A second-order system without zeros must have a step response with 10 % overshoot. Find the damping ratio ζ.

%OS = 10 %
ζ =

Answer key

  1. 1. vC = 3.884 V
  2. 2. y(1) = 15.74
  3. 3. tp = 0.7405 s
  4. 4. ωn = 8.832 rad/s
  5. 5. tp = 3.593 ms
  6. 6. ζ = 0.5912

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