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/(0.5s + 1) receives a step input of size 20 at t = 0, starting from rest. Find the output y(0.1) at t = 0.1 s.

G(s) = 1/(0.5s + 1)U = 20t = 0.1 s

y(0.1) =

2.Easy

An uncharged capacitor C = 4.7 µF is charged from a 10 V step source through a resistor R = 2.2 kΩ. How long after closing the switch does the capacitor voltage reach 90 % of its final value? Find t in ms.

R = 2.2 kΩC = 4.7 µFV = 10 V90 %

t = ms

3.Medium

A system has the transfer function G(s) = 34/(s² + 9s + 68) and receives a unit step input. Find the damping ratio ζ.

G(s) = 34/(s² + 9s + 68)

ζ =

4.Medium

A system has the transfer function G(s) = 141/(s² + 11s + 47) and receives a unit step input. The poles are s = σ ± jω_d. Find the real part σ.

G(s) = 141/(s² + 11s + 47)

σ =

5.Hard

A mass m = 2 kg hangs on a spring k = 2000 N/m with a viscous damper c = 25 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 5 N is suddenly applied. Find the damping ratio ζ.

m = 2 kgk = 2000 N/mc = 25 N·s/mF = 5 N

ζ =

6.Hard

A mass m = 10 kg hangs on a spring k = 5000 N/m with a viscous damper c = 67 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 = 10 kgk = 5000 N/mc = 67 N·s/mF = 50 N

%OS = %

Answer key

1. y(0.1) = 3.625
2. t = 23.81 ms
3. ζ = 0.5457
4. σ = −5.5
5. ζ = 0.1976
6. %OS = 62.12 %

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