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) = 10/(10s + 1) receives a step input of size 5 at t = 0, starting from rest. Find the output y(7) at t = 7 s.

G(s) = 10/(10s + 1)U = 5t = 7 s

y(7) =

2.Easy

A first-order system G(s) = 2/(0.5s + 1) receives a step input of size 2 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 2/(0.5s + 1)U = 2

y(∞) =

3.Medium

A system has the transfer function G(s) = 196/(s² + 4s + 98) and receives a unit step input. Find the peak time t_p of the step response.

G(s) = 196/(s² + 4s + 98)

t_p = s

4.Medium

A system has the transfer function G(s) = 34/(s² + 6s + 17) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 34/(s² + 6s + 17)

%OS = %

5.Hard

A mass m = 2 kg hangs on a spring k = 1000 N/m with a viscous damper c = 13 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 50 N is suddenly applied. Find the largest displacement x_max in mm.

m = 2 kgk = 1000 N/mc = 13 N·s/mF = 50 N

x_max = mm

6.Hard

A series RLC circuit with R = 81 Ω, L = 100 mH and C = 22 µF is connected to a 10 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the time t_p of the first voltage peak, in ms.

R = 81 ΩL = 100 mHC = 22 µFV = 10 V

t_p = ms

Answer key

1. y(7) = 25.17
2. y(∞) = 4
3. t_p = 0.324 s
4. %OS = 3.572 %
5. x_max = 81.52 mm
6. t_p = 5.829 ms

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