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
+−9 VR = 100 kΩC = 1 µFvC​

An uncharged capacitor C = 1 µF is charged from a 9 V step source through a resistor R = 100 kΩ. Find the 10–90 % rise time tr of the capacitor voltage, in ms.

R = 100 kΩC = 1 µFV = 9 V
tr = ms
2.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 0.25/(s + 0.5) receives a step input of size 2 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 0.25/(s + 0.5)U = 2
y(∞) =
3.Medium
t (s)y(t)1tp​ = ?

A system has the transfer function G(s) = 8/(s² + 4s + 8) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 8/(s² + 4s + 8)
tp = s
4.Medium
t (s)y(t)0.5

A system has the transfer function G(s) = 18.5/(s² + 7s + 37) and receives a unit step input. Find the damping ratio ζ.

G(s) = 18.5/(s² + 7s + 37)
ζ =
5.Hard
k = 100 N/mc = 4 N·s/mm = 1 kgF = 25 Nx(t)

A mass m = 1 kg hangs on a spring k = 100 N/m with a viscous damper c = 4 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 25 N is suddenly applied. Find the time tp at which the displacement is largest.

m = 1 kgk = 100 N/mc = 4 N·s/mF = 25 N
tp = s
6.Hard
t (s)y(t)130 %

A second-order system without zeros must have a step response with 30 % overshoot. Find the damping ratio ζ.

%OS = 30 %
ζ =

Answer key

  1. 1. tr = 219.7 ms
  2. 2. y(∞) = 1
  3. 3. tp = 1.571 s
  4. 4. ζ = 0.5754
  5. 5. tp = 0.3206 s
  6. 6. ζ = 0.3579

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