1.Easy
A first-order system G(s) = 5/(s + 10) receives a step input of size 20 at t = 0, starting from rest. How long does the output take to reach 80 % of its final value? Find t.
G(s) = 5/(s + 10)U = 2080 %
t = s
Step response worksheet with answers
2.Easy
A first-order system G(s) = 2/(s + 1) receives a step input of size 2 at t = 0, starting from rest. How long does the output take to reach 50 % of its final value? Find t.
G(s) = 2/(s + 1)U = 250 %
t = s
3.Medium
A system has the transfer function G(s) = 37/(s² + 6s + 37) and receives a unit step input. Find the natural frequency ωn in rad/s.
G(s) = 37/(s² + 6s + 37)
ωn = rad/s
4.Medium
A system has the transfer function G(s) = 102/(s² + 10s + 51) and receives a unit step input. Find the damping ratio ζ.
G(s) = 102/(s² + 10s + 51)
ζ =
5.Hard
A series RLC circuit with R = 170 Ω, L = 20 mH and C = 1 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 = 170 ΩL = 20 mHC = 1 µFV = 5 V
%OS = %
6.Hard
A mass m = 2 kg hangs on a spring k = 5000 N/m with a viscous damper c = 20 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 10 N is suddenly applied. Find the largest displacement xmax in mm.
m = 2 kgk = 5000 N/mc = 20 N·s/mF = 10 N
xmax = mm
Answer key
- 1. t = 0.1609 s
- 2. t = 0.6931 s
- 3. ωn = 6.083 rad/s
- 4. ζ = 0.7001
- 5. %OS = 9.418 %
- 6. xmax = 3.458 mm
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