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) = 1/(10s + 1) receives a step input of size 20 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 1/(10s + 1)U = 20

y(∞) =

2.Easy

A first-order system G(s) = 0.5/(0.2s + 1) receives a step input of size 2 at t = 0, starting from rest. Find the output y(0.3) at t = 0.3 s.

G(s) = 0.5/(0.2s + 1)U = 2t = 0.3 s

y(0.3) =

3.Medium

A system has the transfer function G(s) = 282/(s² + 10s + 94) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 282/(s² + 10s + 94)

%OS = %

4.Medium

A system has the transfer function G(s) = 69/(s² + 4s + 69) and receives a unit step input. The poles are s = σ ± jω_d. Find the real part σ.

G(s) = 69/(s² + 4s + 69)

σ =

5.Hard

A mass m = 2.5 kg hangs on a spring k = 500 N/m with a viscous damper c = 14 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 percent overshoot %OS of the displacement.

m = 2.5 kgk = 500 N/mc = 14 N·s/mF = 50 N

%OS = %

6.Hard

A series RLC circuit with R = 30 Ω, L = 500 mH and C = 22 µF is connected to a 5 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the peak capacitor voltage v_C,max.

R = 30 ΩL = 500 mHC = 22 µFV = 5 V

v_C,max = V

Answer key

1. y(∞) = 20
2. y(0.3) = 0.7769
3. %OS = 15.09 %
4. σ = −2
5. %OS = 53.02 %
6. v_C,max = 8.652 V

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