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 50. At t = 10 s it reads 20. Find the time constant τ.

y(∞) = 50y(10) = 20

τ = s

2.Easy

An uncharged capacitor C = 22 µF is charged from a 24 V step source through a resistor R = 22 kΩ. Find the 10–90 % rise time t_r of the capacitor voltage, in ms.

R = 22 kΩC = 22 µFV = 24 V

t_r = ms

3.Medium

A system has the transfer function G(s) = 154/(s² + 11s + 77) and receives a unit step input. The poles are s = σ ± jω_d. Find the real part σ.

G(s) = 154/(s² + 11s + 77)

σ =

4.Medium

A system has the transfer function G(s) = 28/(s² + 7s + 28) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 28/(s² + 7s + 28)

%OS = %

5.Hard

A series RLC circuit with R = 32 Ω, L = 50 mH and C = 2 µF is connected to a 24 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the percent overshoot %OS of the capacitor voltage.

R = 32 ΩL = 50 mHC = 2 µFV = 24 V

%OS = %

6.Hard

A mass m = 10 kg hangs on a spring k = 100 N/m with a viscous damper c = 32 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 largest displacement x_max in mm.

m = 10 kgk = 100 N/mc = 32 N·s/mF = 50 N

x_max = mm

Answer key

1. τ = 19.58 s
2. t_r = 1063 ms
3. σ = −5.5
4. %OS = 6.262 %
5. %OS = 72.65 %
6. x_max = 579.2 mm

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