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)2.5t = ?80 %

A first-order system G(s) = 0.5/(0.5s + 1) receives a step input of size 5 at t = 0, starting from rest. How long does the output take to reach 80 % of its final value? Find t.

G(s) = 0.5/(0.5s + 1)U = 580 %
t = s
2.Easy
+−9 VR = 100 kΩC = 100 µFvC​

An uncharged capacitor C = 100 µF is charged from a 9 V step source through a resistor R = 100 kΩ. How long after closing the switch does the capacitor voltage reach 95 % of its final value? Find t in ms.

R = 100 kΩC = 100 µFV = 9 V95 %
t = ms
3.Medium
t (s)y(t)3ts​ = ?

A system has the transfer function G(s) = 291/(s² + 11s + 97) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 291/(s² + 11s + 97)
ts = s
4.Medium
t (s)y(t)3tp​ = ?

A system has the transfer function G(s) = 12/(s² + s + 4) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 12/(s² + s + 4)
tp = s
5.Hard
+−5 VR = 83 ΩL = 50 mHC = 4.7 µFvC​

A series RLC circuit with R = 83 Ω, L = 50 mH and C = 4.7 µF is connected to a 5 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 = 83 ΩL = 50 mHC = 4.7 µFV = 5 V
%OS = %
6.Hard
k = 800 N/mc = 101 N·s/mm = 20 kgF = 20 Nx(t)

A mass m = 20 kg hangs on a spring k = 800 N/m with a viscous damper c = 101 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 20 N is suddenly applied. Find the largest displacement xmax in mm.

m = 20 kgk = 800 N/mc = 101 N·s/mF = 20 N
xmax = mm

Answer key

  1. 1. t = 0.8047 s
  2. 2. t = 29957 ms
  3. 3. ts = 0.7273 s
  4. 4. tp = 1.622 s
  5. 5. %OS = 25.14 %
  6. 6. xmax = 31.37 mm

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