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)55 s4

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 5. At t = 5 s it reads 4. Find the time constant τ.

y(∞) = 5y(5) = 4
τ = s
2.Easy
+−24 VR = 1 kΩC = 1 µFvC​

An uncharged capacitor C = 1 µF is charged from a 24 V step source through a resistor R = 1 kΩ. Find the capacitor voltage vC at t = 1.5 ms.

R = 1 kΩC = 1 µFV = 24 Vt = 1.5 ms
vC = V
3.Medium
t (s)y(t)3?

A system has the transfer function G(s) = 24/(s² + 4s + 8) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 24/(s² + 4s + 8)
%OS = %
4.Medium
t (s)y(t)1

A system has the transfer function G(s) = 96/(s² + 9s + 96) and receives a unit step input. Find the damping ratio ζ.

G(s) = 96/(s² + 9s + 96)
ζ =
5.Hard
R(s)+Ks(s + 10)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 10)). Find the gain K that gives a step response with 30 % overshoot.

G(s) = K/(s(s + 10))%OS = 30 %
K =
6.Hard
+−10 VR = 146 ΩL = 100 mHC = 4.7 µFvC​

A series RLC circuit with R = 146 Ω, L = 100 mH and C = 4.7 µF is connected to a 10 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the peak capacitor voltage vC,max.

R = 146 ΩL = 100 mHC = 4.7 µFV = 10 V
vC,max = V

Answer key

  1. 1. τ = 3.107 s
  2. 2. vC = 18.64 V
  3. 3. %OS = 4.321 %
  4. 4. ζ = 0.4593
  5. 5. K = 195.2
  6. 6. vC,max = 11.63 V

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