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) = 2.5/(0.5s + 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) = 2.5/(0.5s + 1)U = 250 %

t = s

2.Easy

A first-order system G(s) = 1/(4s + 1) receives a step input of size 1 at t = 0, starting from rest. Find the output y(0.8) at t = 0.8 s.

G(s) = 1/(4s + 1)U = 1t = 0.8 s

y(0.8) =

3.Medium

A system has the transfer function G(s) = 70/(s² + 13s + 70) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 70/(s² + 13s + 70)

%OS = %

4.Medium

A system has the transfer function G(s) = 22.5/(s² + 5s + 45) and receives a unit step input. Find the 2 % settling time t_s of the step response, using t_s ≈ 4/(ζωₙ).

G(s) = 22.5/(s² + 5s + 45)

t_s = s

5.Hard

A series RLC circuit with R = 6 Ω, L = 100 mH and C = 100 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 = 6 ΩL = 100 mHC = 100 µFV = 24 V

ω_n = rad/s

6.Hard

A series RLC circuit with R = 2 Ω, L = 10 mH and C = 100 µF is connected to a 10 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 = 2 ΩL = 10 mHC = 100 µFV = 10 V

ω_n = rad/s

Answer key

1. t = 0.3466 s
2. y(0.8) = 0.1813
3. %OS = 2.072 %
4. t_s = 1.6 s
5. ω_n = 316.2 rad/s
6. ω_n = 1000 rad/s

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