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) = 25/(s + 5) receives a step input of size 10 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 25/(s + 5)U = 10

y(∞) =

2.Easy

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

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

y(∞) =

3.Medium

A system has the transfer function G(s) = 45/(s² + s + 15) and receives a unit step input. Find the natural frequency ω_n in rad/s.

G(s) = 45/(s² + s + 15)

ω_n = rad/s

4.Medium

A system has the transfer function G(s) = 42/(s² + 5s + 14) and receives a unit step input. Find the peak time t_p of the step response.

G(s) = 42/(s² + 5s + 14)

t_p = s

5.Hard

A series RLC circuit with R = 85 Ω, L = 10 mH and C = 2 µF is connected to a 24 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the undamped natural frequency ω_n in rad/s.

R = 85 ΩL = 10 mHC = 2 µFV = 24 V

ω_n = rad/s

6.Hard

A mass m = 20 kg hangs on a spring k = 400 N/m with a viscous damper c = 18 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 percent overshoot %OS of the displacement.

m = 20 kgk = 400 N/mc = 18 N·s/mF = 10 N

%OS = %

Answer key

1. y(∞) = 50
2. y(∞) = 1
3. ω_n = 3.873 rad/s
4. t_p = 1.128 s
5. ω_n = 7071 rad/s
6. %OS = 72.78 %

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