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/(s + 2) receives a step input of size 10 at t = 0, starting from rest. Find the output y(0.35) at t = 0.35 s.

G(s) = 10/(s + 2)U = 10t = 0.35 s

y(0.35) =

2.Easy

A first-order system G(s) = 0.25/(s + 0.5) receives a step input of size 2 at t = 0, starting from rest. How long does the output take to reach 80 % of its final value? Find t.

G(s) = 0.25/(s + 0.5)U = 280 %

t = s

3.Medium

A system has the transfer function G(s) = 186/(s² + 2s + 62) and receives a unit step input. Find the 2 % settling time t_s of the step response, using t_s ≈ 4/(ζωₙ).

G(s) = 186/(s² + 2s + 62)

t_s = s

4.Medium

A system has the transfer function G(s) = 184/(s² + 6s + 92) and receives a unit step input. Find the 2 % settling time t_s of the step response, using t_s ≈ 4/(ζωₙ).

G(s) = 184/(s² + 6s + 92)

t_s = s

5.Hard

A mass m = 8 kg hangs on a spring k = 800 N/m with a viscous damper c = 96 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 = 8 kgk = 800 N/mc = 96 N·s/mF = 50 N

%OS = %

6.Hard

A unity negative feedback loop has G(s) = K/(s(s + 10)). Find the gain K that gives a step response with 2 % overshoot.

G(s) = K/(s(s + 10))%OS = 2 %

K =

Answer key

1. y(0.35) = 25.17
2. t = 3.219 s
3. t_s = 4 s
4. t_s = 1.333 s
5. %OS = 9.478 %
6. K = 41.12

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