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

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

y(∞) =

2.Easy

A first-order system G(s) = 1/(2s + 1) receives a step input of size 5 at t = 0, starting from rest. Find the output y(4) at t = 4 s.

G(s) = 1/(2s + 1)U = 5t = 4 s

y(4) =

3.Medium

A system has the transfer function G(s) = 252/(s² + 3s + 84) and receives a unit step input. The poles are s = σ ± jω_d. Find the real part σ.

G(s) = 252/(s² + 3s + 84)

σ =

4.Medium

A system has the transfer function G(s) = 183/(s² + 2s + 61) and receives a unit step input. Find the peak time t_p of the step response.

G(s) = 183/(s² + 2s + 61)

t_p = s

5.Hard

A mass m = 10 kg hangs on a spring k = 400 N/m with a viscous damper c = 76 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 time t_p at which the displacement is largest.

m = 10 kgk = 400 N/mc = 76 N·s/mF = 10 N

t_p = s

6.Hard

A mass m = 8 kg hangs on a spring k = 800 N/m with a viscous damper c = 48 N·s/m (m·x″ + c·x′ + k·x = F). At rest in equilibrium, a constant force F = 25 N is suddenly applied. Find the time t_p at which the displacement is largest.

m = 8 kgk = 800 N/mc = 48 N·s/mF = 25 N

t_p = s

Answer key

1. y(∞) = 40
2. y(4) = 4.323
3. σ = −1.5
4. t_p = 0.4056 s
5. t_p = 0.6214 s
6. t_p = 0.3293 s

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