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
+−24 VR = 10 kΩC = 2.2 µFvC​

An uncharged capacitor C = 2.2 µF is charged from a 24 V step source through a resistor R = 10 kΩ. Find the capacitor voltage vC at t = 66 ms.

R = 10 kΩC = 2.2 µFV = 24 Vt = 66 ms
vC = V
2.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 10/(s + 20) receives a step input of size 10 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 10/(s + 20)U = 10
y(∞) =
3.Medium
t (s)y(t)3

A system has the transfer function G(s) = 264/(s² + 11s + 88) and receives a unit step input. Find the damping ratio ζ.

G(s) = 264/(s² + 11s + 88)
ζ =
4.Medium
t (s)y(t)1tp​ = ?

A system has the transfer function G(s) = 55/(s² + 11s + 55) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 55/(s² + 11s + 55)
tp = s
5.Hard
k = 200 N/mc = 48 N·s/mm = 8 kgF = 20 Nx(t)

A mass m = 8 kg hangs on a spring k = 200 N/m with a viscous damper c = 48 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 percent overshoot %OS of the displacement.

m = 8 kgk = 200 N/mc = 48 N·s/mF = 20 N
%OS = %
6.Hard
t (s)y(t)150 %

A second-order system without zeros must have a step response with 50 % overshoot. Find the damping ratio ζ.

%OS = 50 %
ζ =

Answer key

  1. 1. vC = 22.81 V
  2. 2. y(∞) = 5
  3. 3. ζ = 0.5863
  4. 4. tp = 0.6315 s
  5. 5. %OS = 9.478 %
  6. 6. ζ = 0.2155

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