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 = 10 kΩC = 47 µFvC​

An uncharged capacitor C = 47 µF is charged from a 5 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 = 47 µFV = 5 V
tr = ms
2.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 0.5/(s + 1) receives a step input of size 10 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 0.5/(s + 1)U = 10
y(∞) =
3.Medium
t (s)y(t)1tp​ = ?

A system has the transfer function G(s) = 27/(s² + 7s + 27) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 27/(s² + 7s + 27)
tp = s
4.Medium
t (s)y(t)1?

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

G(s) = 24/(s² + 4s + 24)
%OS = %
5.Hard
k = 200 N/mc = 38 N·s/mm = 20 kgF = 100 Nx(t)

A mass m = 20 kg hangs on a spring k = 200 N/m with a viscous damper c = 38 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 100 N is suddenly applied. Find the largest displacement xmax in mm.

m = 20 kgk = 200 N/mc = 38 N·s/mF = 100 N
xmax = mm
6.Hard
R(s)+65s(s + 10)G(s)C(s)−

A unity negative feedback loop has G(s) = 65/(s(s + 10)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 65/(s(s + 10))
ts = s

Answer key

  1. 1. tr = 1033 ms
  2. 2. y(∞) = 5
  3. 3. tp = 0.818 s
  4. 4. %OS = 24.54 %
  5. 5. xmax = 685.9 mm
  6. 6. ts = 0.8 s

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