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/(s + 5) receives a step input of size 1 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 2.5/(s + 5)U = 1

y(∞) =

2.Easy

An uncharged capacitor C = 22 µF is charged from a 12 V step source through a resistor R = 22 kΩ. How long after closing the switch does the capacitor voltage reach 90 % of its final value? Find t in ms.

R = 22 kΩC = 22 µFV = 12 V90 %

t = ms

3.Medium

A system has the transfer function G(s) = 160/(s² + 11s + 80) and receives a unit step input. Find the 2 % settling time t_s of the step response, using t_s ≈ 4/(ζωₙ).

G(s) = 160/(s² + 11s + 80)

t_s = s

4.Medium

A system has the transfer function G(s) = 243/(s² + 4s + 81) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 243/(s² + 4s + 81)

%OS = %

5.Hard

A unity negative feedback loop has G(s) = 195/(s(s + 5)). Find the 2 % settling time t_s of the closed-loop step response, using t_s ≈ 4/(ζωₙ).

G(s) = 195/(s(s + 5))

t_s = s

6.Hard

A mass m = 10 kg hangs on a spring k = 200 N/m with a viscous damper c = 36 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 damping ratio ζ.

m = 10 kgk = 200 N/mc = 36 N·s/mF = 10 N

ζ =

Answer key

1. y(∞) = 0.5
2. t = 1114 ms
3. t_s = 0.7273 s
4. %OS = 48.87 %
5. t_s = 1.6 s
6. ζ = 0.4025

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