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

A first-order system G(s) = 50/(s + 10) receives a step input of size 2 at t = 0, starting from rest. Find the output y(0.15) at t = 0.15 s.

G(s) = 50/(s + 10)U = 2t = 0.15 s

y(0.15) =

2.Easy

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 20. At t = 10 s it reads 12. Find the time constant τ.

y(∞) = 20y(10) = 12

τ = s

3.Medium

A system has the transfer function G(s) = 8/(s² + s + 4) and receives a unit step input. Find the 2 % settling time t_s of the step response, using t_s ≈ 4/(ζωₙ).

G(s) = 8/(s² + s + 4)

t_s = s

4.Medium

A system has the transfer function G(s) = 68/(s² + 9s + 68) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 68/(s² + 9s + 68)

%OS = %

5.Hard

A mass m = 2 kg hangs on a spring k = 400 N/m with a viscous damper c = 11 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 5 N is suddenly applied. Find the largest displacement x_max in mm.

m = 2 kgk = 400 N/mc = 11 N·s/mF = 5 N

x_max = mm

6.Hard

A series RLC circuit with R = 39 Ω, L = 20 mH and C = 4.7 µF is connected to a 24 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 = 39 ΩL = 20 mHC = 4.7 µFV = 24 V

%OS = %

Answer key

1. y(0.15) = 7.769
2. τ = 10.91 s
3. t_s = 8 s
4. %OS = 12.93 %
5. x_max = 19.21 mm
6. %OS = 37.38 %

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