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)103 s7

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 10. At t = 3 s it reads 7. Find the time constant τ.

y(∞) = 10y(3) = 7
τ = s
2.Easy
+−10 VR = 10 kΩC = 4.7 µFvC​

An uncharged capacitor C = 4.7 µF is charged from a 10 V step source through a resistor R = 10 kΩ. Find the 10–90 % rise time tr of the capacitor voltage, in ms.

R = 10 kΩC = 4.7 µFV = 10 V
tr = ms
3.Medium
t (s)y(t)0.5?

A system has the transfer function G(s) = 23.5/(s² + 2s + 47) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 23.5/(s² + 2s + 47)
%OS = %
4.Medium
t (s)y(t)0.5tp​ = ?

A system has the transfer function G(s) = 39.5/(s² + 13s + 79) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 39.5/(s² + 13s + 79)
tp = s
5.Hard
+−12 VR = 20 ΩL = 10 mHC = 1 µFvC​

A series RLC circuit with R = 20 Ω, L = 10 mH and C = 1 µF is connected to a 12 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the percent overshoot %OS of the capacitor voltage.

R = 20 ΩL = 10 mHC = 1 µFV = 12 V
%OS = %
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 30 % overshoot.

G(s) = K/(s(s + 12))%OS = 30 %
K =

Answer key

  1. 1. τ = 2.492 s
  2. 2. tr = 103.3 ms
  3. 3. %OS = 62.93 %
  4. 4. tp = 0.5182 s
  5. 5. %OS = 72.92 %
  6. 6. K = 281.1

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