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 5. At t = 2 s it reads 1.5. Find the time constant τ.

y(∞) = 5y(2) = 1.5

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 = 1 s it reads 20. Find the time constant τ.

y(∞) = 50y(1) = 20

τ = s

3.Medium

A system has the transfer function G(s) = 12/(s² + 7s + 24) and receives a unit step input. The poles are s = σ ± jω_d. Find the real part σ.

G(s) = 12/(s² + 7s + 24)

σ =

4.Medium

A system has the transfer function G(s) = 25.5/(s² + 4s + 51) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 25.5/(s² + 4s + 51)

%OS = %

5.Hard

A mass m = 0.5 kg hangs on a spring k = 500 N/m with a viscous damper c = 9 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 = 0.5 kgk = 500 N/mc = 9 N·s/mF = 25 N

t_p = s

6.Hard

A series RLC circuit with R = 120 Ω, L = 10 mH and C = 1 µF is connected to a 10 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the peak capacitor voltage v_C,max.

R = 120 ΩL = 10 mHC = 1 µFV = 10 V

v_C,max = V

Answer key

1. τ = 5.607 s
2. τ = 1.958 s
3. σ = −3.5
4. %OS = 39.99 %
5. t_p = 0.1036 s
6. v_C,max = 10.95 V

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