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 step is applied to a first-order process at t = 0. The output starts at 0 and settles at 8. At t = 5 s it reads 5.6. Find the time constant τ.

y(∞) = 8y(5) = 5.6

τ = s

2.Easy

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 50. At t = 3 s it reads 45. Find the time constant τ.

y(∞) = 50y(3) = 45

τ = s

3.Medium

A system has the transfer function G(s) = 87/(s² + 11s + 87) and receives a unit step input. Find the peak time t_p of the step response.

G(s) = 87/(s² + 11s + 87)

t_p = s

4.Medium

A system has the transfer function G(s) = 21/(s² + s + 7) and receives a unit step input. Find the peak time t_p of the step response.

G(s) = 21/(s² + s + 7)

t_p = s

5.Hard

A mass m = 10 kg hangs on a spring k = 1000 N/m with a viscous damper c = 40 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 = 10 kgk = 1000 N/mc = 40 N·s/mF = 25 N

t_p = s

6.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 percent overshoot %OS of the displacement.

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

%OS = %

Answer key

1. τ = 4.153 s
2. τ = 1.303 s
3. t_p = 0.417 s
4. t_p = 1.209 s
5. t_p = 0.3206 s
6. %OS = 9.43 %

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